Ash spotted a Mankey in the episode Primeape Goes Bananas and tried to catch it but failed, angering the Mankey in the process. In retribution, it stole his cherished hat, angering Ash. Later, it evolved to Primeape thanks to Team Rocket. Primeape chased Team Rocket and Ash's group, and it eventually finished Team Rocket off. Ash and Pikachu fell into a hole trap dug by Team Rocket. Pikachu used Thundershock on Primeape and Team Rocket. After Squirtle and Bulbasaur failed to weaken it, Ash used Charmander and its newly learned Rage attack to finally weaken it. Ash used his Poké Ball and he successfully captured it.
Ash later thought of using Primeape in his gym battle against Erika, but due to its explosive temper and disobedience, he decided not to use it.
In The Punchy Pokémon, in order to reunite a girl and her training obsessed father, Anthony, Ash entered Primeape in the P1 Grand Prix, the same tournament he was entering. During the tournament, Ash saved Primeape from falling onto the hard floor after being thrown from the ring and in the process finally gained its respect. After winning the P1 Grand Prix, Ash left Primeape to train with Anthony to become a true P1 Champ.
According to Ash's Squirtle's wiki page, Primeape is to reappear in an upcoming episode of Best Wishes Season 2 along with Ash's Charziard and Squirtle.