Here are some of the major episodes where Ash participates in the League:
* Indigo League: The Indigo League is Ash's first major tournament, starting with episode 117, "The Power of One". It culminates in the final battle with Gary in episode 128, "The Final Battle!".
* Orange Islands: Ash participates in the Orange Islands League, which is a smaller competition with a more specific focus on Water-type Pokemon. This occurs in season 2, starting with episode 132, "A Wilderness of Orange".
* Johto League: The Johto League is Ash's second major League, starting in episode 191, "A Tail of Two Cities". This culminates in the final battle with Harrison in episode 264, "The Final Frontier!"
* Hoenn League: The Hoenn League is another major League that Ash competes in, starting in episode 341, "A League of Their Own". This culminates in the final battle with Tyson in episode 392, "Advance to Victory!"
* Sinnoh League: Ash's journey in Sinnoh culminates in the Sinnoh League, which starts with episode 443, "The Bells Are Ringing!" It concludes with the final battle against Tobias in episode 488, "A Hero's Outcome!"
* Unova League: Ash's journey in Unova sees him compete in the Unova League, starting with episode 530, "The Lost Clash!" The League culminates with the final battle against Cameron in episode 609, "A Farewell to the Unova League!".
* Kalos League: Ash's journey in Kalos sees him competing in the Kalos League, starting with episode 661, "A League of Our Own!" The League culminates with the final battle against Alain in episode 708, "The Final Showdown!"
* Alola League: Ash's journey in Alola features the Alola League, starting with episode 740, "All Alola, on the Show!" The League culminates with the final battle against Gladion in episode 767, "A Fighting Spirit!"
You can find more information about the League and individual episodes on the official Pokemon website or the Pokemon Wiki.