Pikachu
Ash's first and main Pokemon. It dislikes Pokeballs, so it hangs out with Ash all the time, usually travelling on his shoulder, hat or just walking alongside. As such, the two develop a strong friendship, and Ash cares about Pikachu more than any human.
The two did not have a very good first meeting, as Pikachu did not like humans, or being trained, but it learned to respect and appreciate Ash after he saved its life.
Pikachu is unusually strong, surely stronger than normal Pikachu. I would put this down to:
a) the charge it received from Misty's bike light
b) the increase in power that Flint helped Ash to give it
c) the fact that it is always outside its Pokeball and thus becomes stronger with regular exercise
d) the fact that Ash uses it often
This strength is what attracts Team Rocket to it, and it is the reason the Rockets follow Ash around everywhere, to steal it.
It electrocutes with little provocation, and Team Rocket often learn to insulate their suits or vehicles as they are still weak to electricity. Pikachu can also have difficulty controlling its electric powers, sometimes zapping its friends as well as its foes.
Pikachu makes friends with other Pokemon easily. It is generally good tempered, and very loyal to Ash. It is also quite gutsy, fighting hard in almost any circumstance, although it has been known to conveniently take a nap just as Ash proposes an impossible challenge! Due to this bravery, it is also not a good loser. Pikachu reflects its trainer's personality in many ways.
Few Pokemon have ever beaten Pikachu, who can even defeat some ground types. But it has happened.
Caterpie/Metapod/Butterfree
Ash caught a wild Caterpie without weakening it first, much to Misty's disgust - she hates bugs. But Ash likes them, and it was his very first Pokemon. Happy at having caught it, he let it free of its Pokeball for a while, and made friends with it. Caterpie dreamed of becoming a beautiful Butterfree and being able to fly. It also liked Misty, but Misty was scared at it and was thus mean to it, which saddened Caterpie. But it managed to win her respect after tying Team Rocket up with String Shot.
After this battle, Caterpie evolved into Metapod. Ash sent his Metapod into a long and boring battle against another Metapod, but a swarm of Beedrill came and Ash got seperated from his Pokemon. He did not go back to get it, but his conscience got the better of his fear, and he snuck in amongst a lot of bee Pokemon to rescue Metapod. Metapod was angry at Ash for abandoning it, but Ash managed to convince it of his sincerity, and Metapod evolved to Butterfree to put all the Beedrill to sleep and save its master.
Butterfree was one of Ash's favourite Pokemon, while he had it. It was strong, for a Butterfree, and fought bravely. But Butterfree fell in love with a cute pink Butterfree. This Butterfree did not return its feelings, but Ash's managed to win her heart by saving her from Team Rocket, showing its guts, love and perseverance.
Ash let Butterfree go for its mating season with the pink Butterfree. He never saw it again.
Pidgeotto/Pidgeot
Soon after catching Caterpie, Ash managed to catch a wild Pidgeotto. This bird was reasonably strong, but Ash did not use it very often. In fact, with a couple of exceptions, he didn't use it in battle, just for a) gusting Koffing/Weezing's smokescreen away, b) flying after Team Rocket's balloon.
Pidgeotto, being Ash's only flying type (after Butterfree left), was used whenever a flying Pokemon was needed, not to fight. It might scout territory to find a path or dry land or where Team Rocket went, or it might fly after Team Rocket if they are escaping by air, but beyond that...
It's a shame. :(
However, despite Ash's complete lack of attention to this bird, it did evolve. It wanted to help its own kind; Pidgey and Pidgeotto were being terrorised by a very strong Fearow, and a flock of Spearow. The Fearow beat Pidgeotto, but it retaliated by evolving and fighting back! Ash left Pidgeot to stay with the Pidgey and Pidgeotto near Pallet.
Bulbasaur
This Pokemon was a gutsy, sturdy sort who guarded a village for sick and injured Pokemon. It made sure no trainers caught Pokemon from there. However, the owner of the village gave Bulbasaur to Ash, saying that Bulbasaur needed to be able to grow strong and travel. Bulbasaur would not allow itself to be given to Ash until Ash could prove he was a worthy trainer by defeating it, which he duly did.
Bulbasaur had difficulty in trusting Ash at first, even once thinking that Ash abandoned it, but after a while, its loyalty grew. Its personality was bitter, finding it difficult to trust humans, but that changed, particularly after a certain important episode in Bulbasaur's life...
There is an evolution festival in a mysterious garden where Bulbasaur gather each year to evolve into Ivysaur. When Ash found out that his Bulbasaur was ready to evolve, he was thrilled... but Bulbasaur did not seem too happy. Although Bulbasaur did go to the mysterious garden - not by choice - it refused to evolve. All the Ivysaur, and the Venusaur that was overseeing the evolution festival, became angry at Bulbasaur for ruining their ceremony.
However, Ash ran to save his Bulbasaur, facing an angry group of seed Pokemon, saying that it was Bulbasaur's choice if it wanted to evolve or not. He apologised to Bulbasaur for not considering its feelings regarding evolution. At around that time, Bulbasaur learned its strongest attack - Solar Beam - proving that it could be strong even if it did not want to evolve.
It is not known why Bulbasaur did not evolve, but I suspect it just likes being what it is, and did not want to turn sour like Charmander did.
Now, Bulbasaur is one of Ash's most faithful Pokemon, and stays on his team.
Charmander/Charmeleon/Charizard
Charmander was tricked by its former trainer, Damien, who wanted to rid himself of the "weak" Pokemon and could only do so by convincing it that he would come back for it. Charmander waited for its trainer to return, but he didn't, and Brock rescued it. However, Charmander was loyal and wanted to keep waiting for Damien. It finally realised that Damien did not care about it, and went with Ash.
Charmander was Ash's 'torch', being used to light up caves and the like. It also was good for burning holes in things, as well as being Ash's strongest Pokemon, besides Pikachu; Ash used it often. Despite its past, it knew Ash cared about it and wanted to do its best for him. It was also the most good-tempered of Ash's Pokemon.
However, after beating a lot of Exeggutor, Charmander EVOLVED.
Charmeleon had a different personality and a bad attitude. It refused to listen to Ash, and wanted only to battle. Because of desire to win a battle, it evolved into Charizard. Charizard was just as bad.
Charizard did not hate Ash, it simply disrespected him, and mostly ignored him. If Ash needed it, it would usually come out of its Pokeball and go to sleep - unless it saw a challenge it really wanted to accept. Ash could not train it properly; Charizard's disobedience cost him the possibility of becoming a Pokemon Master. However, if it did want to fight, it accepted that Ash knew what he was doing, and listened to his commands.
Although Charizard never listened to Ash, the boy kept it on his main team, possibly out of hope? And, finally, Charizard does learn to listen to Ash once more...
Squirtle
Ash's Squirtle was abandoned by its original trainer, and formed a group with some other Squirtle who were disillusioned with humans. They called themselves the Squirtle Squad, and they played nasty pranks on people. But even after Squirtle was mean to Ash, Ash saved its life from Team Rocket, and it decided to go with him.
Squirtle wore a pair of big sunglasses when it was leader of the Squad. Whenever it is around other Squirtle, it puts the sunglasses on (so that the viewer can distinguish). It keeps them inside its Pokeball. ^_^.
Squirtle is a bit of a smart-alec, a bit of a tease, but accepted Ash immediately, and helps him out all the time. It is faithful, fights strongly - and although Ash does not use it to fight as much as other Pokemon, it is strong. Like Bulbasaur, it believed that Ash might have abandoned it - having had it happen to it once before - but was reluctant to accept it at first.
Whether or not Squirtle will evolve is something of a mystery. I do not think it will, but it has never shown that it is unwilling to. Now, it stays on Ash's main team.
Krabby/Kingler
Ash caught a Krabby without much effort, in order to prove that he could catch Pokemon. This Krabby went to Professor Oak, and stayed with the professor, helping him with his poetry and doing things for him. Although Ash had never trained it, he chose it for a Pokemon League battle - against everyone else's advice.
His faith in the Pokemon he barely knew paid off. Krabby beat an Exeggutor (?!) and evolved. Kingler was powerful, and Ash used it in several Pokemon League battles, most of which they won. But then he left it again, not keeping it on his main team.
Muk
Ash caught a wild Muk in a power plant that was wreaking (or reeking!) havoc. Professor Oak was not thrilled to receive such a bad smelling Pokemon, but I suppose he adjusted, and the two became friends. Muk is a very affectionate Pokemon, which has the unfortunate tendency to glomp onto anyone it likes. ^_^.
It also won Ash an important victory in Pokemon League.
Tauros
In a cut episode, Satoshi (Ash) went to Safari Zone and caught a lot of these Pokemon by mistake. Whenever he threw a Safariball to catch a wild Pokemon, a herd of Kentauros (Tauros) ran in front, and he would accidentally catch one of them instead. When Professor Ookido (Oak) told him to catch Pokemon, I don't think he quite meant this! The herd nearly trampled him!
Takeshi (Brock) caught a Kentauros also, but it was never shown again; my guess is that it went to Ookido with Satoshi's Pokemon.
Ash's Tauros are shown with little introduction - it can be confusing, because the English version never showed him catching them. However, his herd of Tauros drive off Team Rocket and break a fence.
Lapras
This Lapras was rescued from abuse by Ash and his friends, but would not trust any humans. After Ash risked his life to save Lapras from Team Rocket, this Pokemon decided to trust him and went with him as his Pokemon.
Ash and his friends use Lapras as their mode of transportation, riding on its back, in the Orange Islands. It is on Ash's main team, and is used fairly often, sometimes in battle too. It is a fast swimmer.
Lapras is a gentle, kind-eyed Pokemon, but it can show determination too, when it counts, and is more convenient than any boat. Ash always gives it a rest in its Pokeball when the group are on land.
Snorlax
Ash caught it after a lot of effort. It was strong enough to withstand all attacks, but finally fell asleep from Jigglypuff, and Pikachu was the only one that could weaken it enough to allow Ash to capture it. This Snorlax was gutsing itself on grapefruits that had taken people a lot of effort to grow; it ate loads and loads of them, destroying their livelihood. Ash caught it as a means of stopping it. Now it is on his main team.
Goldeen
Misty's water Pokemon is not shown often, and she battles with it rarely, but it seems fairly strong nonetheless. It is incapable of fighting on land. Sometimes it is just used whenever a water Pokemon is needed - to tow a boat, to search for something/someone underwater, etcetera.
Staryu
Misty's primary battling Pokemon. This Pokemon is strong, determined and fights well. It hurls itself spinning through the air, can stand on two of its legs, or swims. It is also used as Goldeen is; when a water Pokemon is needed.
Although it and Starmie do not have faces, Misty can tell when they are hurt or feeling bad, because she understands them.
Starmie
Probably Misty's strongest Pokemon, she raised it and it battled well. However, her sisters needed more water Pokemon in Cerulean Gym to perform in water ballets, and Misty reluctantly left this Pokemon with them.
Horsea
Misty caught it after it had tried to warn them about dangerous Tentacool. It is small and inexperienced, and does not battle well. However, its ink has proved useful once or twice; it is a smart Pokemon. It likes to have a large area to swim in, so Misty left it with her sisters in Cerulean Gym to help them in their water ballets.
Psyduck
This Pokemon in Hop-Hop-Hop Town was the only one that did not lose its headache after the hypnosis wore off. Brock, smitten with Nurse Joy, offered to take care of it, but he didn't really want it. He suggested Misty take it, as she was a water Pokemon trainer, but Misty really didn't want it. However, Psyduck snuck into a Pokeball anyway.
Psyduck is an odd Pokemon. It is not well-trained, and is extremely stupid, being incapable of properly listening to Misty, even forgetting its own attacks. It is clumsy, slow and weak. Also, it suffers from a continual bad headache, which pains it, but it's also the key to its power.
When Psyduck's headache becomes extreme, it realises its ability to use Disable and Confusion - powerful attacks that always work strongly - WHEN they work! This ability is probably the only reason Misty keeps Psyduck, given that it can be useful, although she does have a soft spot for it.
Psyduck comes out of its Pokeball without being called, which often works to Misty's disadvantage, as the opponent can easily beat Psyduck if they don't inspire a migraine. This, accompanied with Psyduck's constant blank look and "uselessness as a water type", makes Misty very annoyed at it. She shouts at it and insults it a lot.
Misty once thought that Psyduck evolved, but it was a wild Golduck. Misty loved Golduck; Golduck are one of her favourite Pokemon species, and she was devastated to find out her Psyduck was still a Psyduck. Apparently, it decided not to evolve - poor Misty!
It is also different from other Psyduck, having no control over its psychic powers, being stupid, and not being able to swim. But it has its charm - when it isn't quacking incessantly and whining in pain!
When it does come out, Psyduck often proves itself more powerful than any other Pokemon, and has won near-impossible battles. Misty would never trade it or abandon it, despite the headaches Psyduck so frequently gives her! ^_^.
Togepi
Ash found an egg in Grandpa Canyon and took it. Brock looked after it, but after it hatched, there was a fight over who should get to keep it. Misty eventually acquired it, and constantly has the baby Pokemon in her arms.
Togepi is nearly completely helpless, it can barely walk on its tiny legs. It behaves like a baby; cries sometimes, mindlessly smiles/chirps or looks concerned, just watches everything and looks cute. However, Misty cares about it a great deal and treats it well. Pikachu also acts as a togesitter.
Because Togepi is a baby, and thus stupid, it does some pretty dumb things, not realising the danger. Examples include managing to climb to a high beam outside a blimp several thousand feet high, toddling towards the edge of a volcano, and nearly impaling itself with cutlery. In these cases, Pikachu or Misty rescue it.
Togepi has a rather cute feature; when it is hurt, dazed, unconscious or asleep, it curls the spines of its head in and makes a complete egg shape. It seems almost incapable of feeling pain.
Recently, Togepi has displayed some power, using Metronome to do Explosion, Barrier and Teleport, all of which were executed powerfully. The humans are largely unaware of this hidden power, although Misty suspects that Togepi may know Metronome.
Jigglypuff
Jigglypuff is a wild Pokemon, not owned by anyone. Misty tried to catch it (haha, if she had caught it, she would have all three repetitive Pokemon - Psyduck who makes a nuisance of itself, Togepi who obliviously endangers the lives of others, Jigglypuff who always...), but stopped after seeing Jigglypuff's unhappy predicament - it couldn't sing.
After Brock helped it to be able to sing, it overcompensated. Jigglypuff became obsessed with singing, always wanting to perform. It used a thick black pen as its microphone, but would always trail off in the middle of its song, because the unhappy situation is... a Jigglypuff's song is an attack that makes people fall asleep!
Jigglypuff gets angry and offended when people fall asleep during her song, and scribbles on their faces with her pen. She loves that pen, it is her favourite possession. Jigglypuff follows Ash and his friends around, constantly causing trouble for them. But they care about it anyway, even if it is mean. ^_^.
Geodude
One of Brock's first Pokemon, it didn't seem to be very strong. It was defeated by an electric attack from Pikachu. It was defeated by a poison attack from Koffing. >_<. You get the idea. However, it wanted to do well for its trainer, and came in useful a few times. Brock once entered it in a tournament for fighting Pokemon, but Geodude is WEAK against fighting-types, so... it didn't do too well!
Onix
Brock's strong, huge rock Pokemon whose pure length has given it advantages over other Pokemon. It is quite fast for an Onix, doing well in a Pokemon race (until it reached the water section of the course). It is extremely vulnerable to water, and Meowth managed to beat it with this in mind.
Zubat
Brock caught one outside Mount Moon. It was attacking Seymour in broad daylight, confused because lights had been strung up in the cave, where it should have been dark. Brock very rarely used it, just once or twice for reconnaisance.
Vulpix
A famous fashion model Pokemon raised by star breeder Susie. Susie gave it to Brock, knowing that he could bring out its inner strength and personality even more. It was Brock's favourite Pokemon, and extremely powerful. He liked brushing its tails, and refused to evolve it by force.
Ekans/Arbok
Jessie's first and main Pokemon, she got it for her birthday. She cares about it a lot, and vice versa, but mostly just orders it around. Ekans was a decent fighter but lost frequently, only evolving because it knew Jessie appreciated it. Arbok, although consistently defeated by Pikachu, is actually pretty powerful, and well-trained, knowing a lot of attacks, ranging from Toxic to Dig, from Double Edge to Poison Sting.
Ekans and Arbok, being my favourite Pokemon, earned the right to have a site for them. Venom, the snake shrine of barren updates. If you want more info on them, some is there.
Lickitung
A wild Lickitung wandered up and started chewing up a lot of clothes that Jessie had just bought. Jessie, becoming angry, hurled a Pokeball at it and caught it! Lickitung proved to be exceptionally strong, its tongue-lashing causing paralysis and instant victories. She does not use it to battle quite as often as Arbok.
Koffing/Weezing
James got Koffing for his birthday. The two got along well, and Koffing evolved when it realised James cared about it. Weezing is fairly strong as a fighter, but is more often used to create a diversion, using smog or smokescreen to cloud up an area.
Weezing, being a villain's Pokemon, is not allowed to win very often, if at all. It is usually used in conjunction with Arbok, and the two fight reasonably well together, although they lose.
Victreebell
James had a Weepinbell and put it in Butch and Cassidy's breeding center, where it evolved. Where he acquired Weepinbell is not known; presumably he just stole Victreebell from the center.
Victreebell is a powerful grass Pokemon that executes its moves strongly - when it chooses to. It has an incurable habit of sucking James' head into its mouth and eating him. ^_^;; As Meowth said, "train that thing!" It does generally listen to him, even if it can't resist a blue-haired snack. ^_^.
Growlithe
James' first Pokemon, he had Growly, a Growlithe, as a child. He and the puppy were great friends, in fact Growlithe was his only true friend in his younger years. However, after James ran away from home, he left Growlithe to stay and take care of his parents. Maybe he didn't want to take his best and first friend with him in the consistent failure of Team Rocket.
Magikarp/Gyarados
James was conned into buying a Magikarp, but it was weak. It couldn't swim to save their lives (literally), and was inedible. This so frustrated James that he finally kicked the useless, expensive carp into the sea, where it angrily evolved into Gyarados. Gyarados sent everyone flying with Dragon Rage, and James never did manage to keep it. ^_^;
Chansey
Chansey work in Pokemon Centers, caring for sick and injured Pokemon. They are nurse Pokemon, assistants to Joys. This probably stems from their ability in the game to learn Softboiled, a move that will heal other Pokemon.
Chansey are level-headed and kind, working diligently and always caring about injured Pokemon.
