Samurai only shows up once, in "Challenge of the Samurai." He's a trainer from Pallet Town who's apparently got a chip on his shoulder—he'd already lost to Gary and two other Pallet trainers, so when he spots Ash and Misty in Viridian Forest, he jumps out of the bushes waving a sword around and demands to know where they're from. Once he finds out Ash is also from Pallet, he immediately challenges him to a battle.
The fight gets messy fast. Ash was about to catch a Weedle when Samurai showed up, and in all the commotion with the sword-waving and yelling, the Weedle bolts. Samurai takes this as proof that Ash is a "bad Trainer" and won't let it go. His Pinsir demolishes Ash's Pidgeotto, but then things get ridiculous—Ash's Metapod and Samurai's Metapod end up in a total stalemate, both just using Harden over and over for hours because neither can do anything else.
A swarm of angry Beedrill (mad about that Weedle incident) crashes the party and kidnaps Ash's Metapod. The three of them hide out in Samurai's cabin, where he keeps insulting Ash for not immediately jumping in to help. But Samurai finally shows him some respect when Ash's Metapod evolves into Butterfree and puts the whole swarm to sleep with Sleep Powder.
They part on decent terms, both saying they'll battle again someday. He also made a quick cameo with his Pinsir in the second opening theme, "The Rivals."
Content compiled by AnimeList.moe from publicly available sources.