Ash caught Primeape on Route 7 in the episode Primeape Goes Bananas. On the road to Celadon City, Ash learned that Gary had already caught 30 Pokémon. Upon hearing this, Ash aspired to catch more for himself. Soon afterward, a friendly wild Mankey ate some of Brock's food. Ash took this opportunity to try to catch the Pokémon, but the Poké Ball failed, instead catching a rice ball. Mankey was angered and chased the group, beat up Ash, and stole his hat. Mankey gleefully teased Ash as the young Trainer fumed about having his beloved cap stolen. Team Rocket took this opportunity to make a plan to capture Pikachu, with Mankey walking up to Team Rocket. James kicked it out of sight and this angered the Pig Monkey so much that it evolved into Primeape. It proceeded to punch Jessie in the face, sending her face-first into a rock, then viciously attacked the Team Rocket members. After it beat up Brock, chased Ash and Misty down Route 7 and followed Ash into one of Team Rocket's pitfalls, Ash made several attempts to catch the rampaging Primeape, and eventually, his Charmander was finally able to defeat it. Ash caught it and unleashed it upon Team Rocket, where it brutalized them and sent them blasting off into a nest full of wild Primeape.
It appeared in a flashback in Pokémon Scent-Sation! and was planned to be used against Erika. However, Ash decided not to when he recalled how crazy it was.
In The Punchy Pokémon, after leaving Celadon City, Ash and his friends met a man named Anthony who was training to win the P1 Grand Prix, a tournament for Fighting-type Pokémon. Anthony's daughter, Rebecca, wanted him to stop spending so much time away from home training. Brock and Ash volunteered to enter the tournament to discourage Anthony, with Ash entering Primeape. In the first match against a Machop, Ash saved Primeape from a nasty fall, which caused the usually angry Pokémon to become closer to Ash. Primeape eventually won the tournament. Anthony offered to train Primeape for Ash, with the promise of training it to become a P1 champion, so Ash left Primeape with Anthony. Primeape, unlike the other Pokémon that Ash has given to another Trainer for training, hasn't been seen since (although the narrator in the dub hinted at the end of the episode that it's possible that Primeape would return).
Primeape was only around for a few episodes, but it had a lot of personality. It was very mischievous, mercilessly vicious, extremely violent, almost always out of control, had a very short fuse and was prone to an explosive rage. This notably caused Ash to audibly reconsider using Primeape in a Gymbattle against Erika. But under the explosively violent personality, it had a softer side, which allowed it to bond with Ash.
A † shows that the move was used recently, unless all moves fit this case or there are fewer than five known moves.
In the manga
Mankey with its group in The Electric Tale of Pikachu
In The Electric Tale of Pikachu manga
Ash's Mankey appeared in Clefairy Tale. It was initially a member a larger group of Mankey pursued in a forest by Ash and his Fearow. After Fearow cut the Mankey off and Pikachu attacked them with Thunder Shock, the Mankey panicked and slammed into a Beedrill nest, causing both groups to be attacked by a swarm of angry Poison Bee Pokémon. Later, after finding out that his Mankey was only a Grade D capture, a disappointed Ash started walking around and came across a man who offered him a map of Mt. Moon to find Clefairy. Ash offered the man his Mankey in exchange for the map, only to later find out that the map was false and that he had been scammed.