Ash caught these pokemon in the Kanto Region/seafoam islands.
Pikachu-given to him in the first episode by Oak, this is Ash's starter pokemon.
Caterpie/metapod/butterfree-Caught in the episode "Ash catches a pokemon" It soon evolved into a metapod and then Butterfree a few episodes later. He traded it for a raticate on the SS anne, only to trade it back soon after. He releases it in the episode "Bye Bye butterfree."
bulbasaurthis one was caught in "Bulbasaur and the Hidden Village." despite being fully unevolved, it stands as one of his strongest pokemon.
squirtle- caught in "Here Comes the Squirtle Squad," squirtle was a member of a gang known as the squirtle squad. He went back with them, but would be ready to come back if Ash needed him.
raticate- He had this one very shortly. He got it via trade from a guy on the SS anne. He later traded his Butterfree back though.
Haunter-Not officially caught by Ash, but he met him in "the tower of terror." He used it against the psychic gym leader Sabrina, and it stayed with her.
Primeape -Ash found it as a Mankey when it stole his hat. It soon evolved and he caught it in the episode "primeape goes bananas. " He later entered it in a fighting pokemon tournament and left it for training with one of the people there in "the punchy pokemon.
Krabby/Kingler-He caught it in "the mystery of the lighthouse. He didn't use it very freuquently, and it evolved into Kingler during his Kanto league battles. It is currently with Prof. Oak at his lab.
Charmander/Charmeleon/Charizard-Caught in "Charmander: the stray pokemon," this quickly became on of Ash's most powerful pokemon. As it evolved, it started to become more and more disobedient. After Ash cared for it following being frozen and humiliated, it gained a newfound respect for ash. It resides in the Charific Valley and can be called on by Ash during his toughest battles.
Pidgeotto/Pidgeot- caught in "Ash Catches a pokemon," this was one of Ash's first pokemon. It evolved into pidgeot in the episode "Pallet Party Panic," where ash released him.
Lapras- Ash caught lapras in the episode "The Lost Lapras." It was mainly a means of travel for the orange island segment. It was later released in the episode "viva las Lapras."
Tauros (30) Caught in the safari zone of a banned episode of pokemon.
Muk-Caught in "sparks fly for magnemite, Muk was the leader of the grimer terrorizing Sunny town. Ash dispatched it and decided to catch it.
snorlax-This powerhouse was caught in the episode snack attack.
I know this isn't just season one, but Kanto region as a whole paired with the Orange island saga.
All of his pokemon can be seen here. You can also see any anime trainer's pokemon here.