End of Evangelion
Asuka vs Mass Production Evas. I loved End of Evangelion and one of the reasons was Asuka's battle against the white evas that showed up to battle NERV. Although it didn't end well for Asuka, it was still a great battle showing off what the evas can really do.
Samurai Champloo
Final battles. It's so difficult to narrow down the fights in Samurai Champloo, there are so many that are great in this series, but I really loved how the final battles turned out. Jin had to be unpredictable and Mugen had to think a bit more.
One Piece
I have a lot for One Piece, so I won't go into full detail and will just list them.
Zoro vs Mr. 1
Sanji vs Bon Clay
Luffy vs Lucci
Zoro vs Kaku
Digimon Tamers
Gallantmon vs Beelzemon, this fight really proves how awesome and deep this Digimon series was. The emotion, the animation, the characterization was all there. It was fantastic.
Dragon Ball Z
Goku vs Frieza. Yes it went on forever, but what an epic fight this was. The super spirit bomb not working, Goku finally reaching super saiyan status and a finale taking place on a planet minutes (hours?) away from exploding. It's hard to top and I don't know if I've enjoyed any DBZ fight more.
Gundam Wing
Wing Zero vs Epyon (Heero vs Zechs). While it's probably not the most well liked Gundam series, the final Gundam Wing fight is pure nostalgia for me. This battle had been hyped up the whole series and the end result was great.
Yu Yu Hakusho
The Dark Tournament. This is a bit of a cop out, but it's too tough to choose. All the fights in the Dark Tournament were done right in my opinion, delivering a entertaining, satisfying arc. It's especially good since the final bouts lived up to the hype.
Escaflowne the Movie
Final battle. The final fight between the guymelefs in the feature film retelling of Escaflowne was epic and really provided a battle that the series never could. Every blow that the giant mechs throw at each other can be felt. It's really exciting.