When Ash and his friends arrived at the Grapefruit Islands, they discovered that a Snorlax was eating every grapefruit in the orchards. Eventually, the group, with help from Jigglypuff, managed to stop Snorlax and Ash as well managed to catch it.
Snorlax remained on Ash's team right up until the Orange League final, where it had to be switched with one of Ash's Tauros because it would not wake up. After Ash won the Orange League, he left Snorlax at Prof. Oak's lab on a permanent basis, as he could no longer fuel its large appetite.
In Ring Masters, Ash used Snorlax in the Sumo Conference and it ended up winning. Later on, in Better Eight Than Never, Ash used Snorlax against Clair's Kingdra and it won the battle. During the Johto League, Ash used Snorlax in his battle against his long-term rival Gary Oak. Snorlax defeated Gary's Nidoqueen and Arcanine before being defeated by Gary's Scizor. Snorlax was also used in Ash's next battle against Harrison and defeated his Steelix and Hypno, but was knocked out by Harrison's Houndoom.
Snorlax reappeared in An Old Family Blend, where it had gone missing from its Poké Ball, like Ash's other Pokémon. Snorlax was found in the kitchen eating food. Ash tried to use it to battle Team Rocket, but it refused to wake up and accidentally tipped over Team Rocket's mecha. Snorlax was shown defeating an unknown Trainer's Grumpig with Body Slam during the Sinnoh League.
Snorlax will reappear at the lab with all of Ash's other Pokemon in an upcoming episode of Best Wishes Season 2.