RPG's of any kind. I adore plot-driven games and any kind of RPG battle system generally appeals to me, whether it be real-time or turn based.
Strategy (RPG's) - games like Fire Emblem, Disgaea, and Final Fantasy Tactics. RPG's with strategy elements. The best S-RPG's seem to be among my favorite games, and tend to have the best stories, in my opinion, at least.
Action/Adventure games. Tenchu, Zelda, Starfox (the starfighting ones, anyways)- that kind of stuff. Fun games that rely more on gameplay than plot - but still have a good backstory.
Yeah, I'm all about storylines. I love a good story in a game. Coupled with great gameplay - and you've got a kick-ass game, that you do.
