Back when I watched the anime I really enjoyed Ash vs Gary (Johto League), Ash vs May (Advanced Gen Finale), Ash vs Nando (Sinnoh League), Ash vs Conway (Sinnoh League), Ash vs Paul (Sinnoh League), Brock vs Saturn and Dawn vs Zoe I think her name was (Sinnoh Grand Festival). Basically I really loved Sinnoh and remember it much more clearly than the others but a few earlier ones have stuck with me lol.
I also really liked Mew vs Mewtwo, Charizard vs Entei and Dialga vs Palkia (vs Darkrai) from the movies.