
Kimi ga Nozomu Eien. I think it's for the PC. The anime is based on the game. It's only in Japanese.
Why the twisted, you ask? That's because KGNE is an ero-game!
There's a RahXephon PS2 game, I believe. Comes with an OAV.
There is at least one Naruto game and another coming out.
There are, obviously, the .hack games.
Kanon. Anime based on the game, again. Dating sim, maybe ero, I believe.
There's at least one Shaman King game.
Oodles of Yu-gi-oh games, but they're all card battle games, as far as I know.

Chrono Cross and Chrono Trigger. Chrono (Chrno) Crusade was based at least loosely on them, I think.
Ragnarok Online. Ragnarok: the Animation was based at least loosely on it.
Orphen (PS2) - there's an anime with Orphen in the title, looks related.
There's a Lodoss game for the Dreamcast.
At least one One Piece game.
There is, or is going to be, a Berserk PS2 game.
And, of course, the Ghost in the Shell: Stand Alone Complex game.
....I've never played any of these, though.