My favorite video games based on an anime:
Hajime no Ippo PS2 boxing games: The first one came out in the US under the titled "Victorious Boxers". I usually don't like boxing games, except SNES Super Punch-Out!! (and, to a lesser extent, Punch Out for NES), but I found the PS2 boxing games to be very fun.
Hajime no Ippo GBA boxing game: Treasure (responsible for Gunstar Heroes, Guardian Heroes, Dynamite Headdy, and other quality titles) made this and its awesome. I actually like the GBA game better than the PS2 Ippo games.
One Piece Grand Battle 2: I'd probably like Grand Battle 3 if I had it, but I do own this import title on PS1, and I like it a lot. I wouldn't rate it up to par with some of my favorite games ever, but its pretty fun stuff.
I also enjoyed the Berserk Dreamcast game. I thought it stayed true to the manga, even though it had an all new storyline. The gameplay was decent, too. I haven't played the newer PS2 Berserk game, though.