I really liked the story to Valkyria Chronicles...it follows some anime tropes, but it really does have some likable characters there. The story to the Starcraft series is another good one.
I do like the Halo storyline due to the fact that it is a combination of ever sci-fi story out there. However I would ague that the Mass Effect series has the best storyline, especially since you can alter the way it plays out.
Bioshock is the obvious one but its has an amazing story. Bioshock 2 has a good story too but it wasnt as good as the first one. I mean the first one had crazy plot twists, Best story so far.
Are we talking complete fantasy sci-fi, medieval, or realistic this-could-be- happening edge?
I will nominate either Halo or Mass Effect for having the best sci-fi. Each is incredibly deep, if you take the time to look into it.
For medieval fantasy, probably Fable, Dragon Age, or Elder Scrolls. The only one I've actually played is Fable, and only a little bit at that. But they all seem almost as incredibly deep as the two above.
For realism... I haven't played that many games. I don't think GTA is a valid option, as it's story is...not really deep. You play the part of a gang member. That's about it. I've heard, in recent posts either Bioshock or MGS. I guess I'll put them here, having no experience with either one.
I don't think it's fair to not break this competition up into categories.
hmmm... both Final Fantasy VII and Final Fantasy Tactics have great stories. and cant forget about Chrono Trigger.. I would say zelda but most of them have pretty much the same story.. kinda..
lol... im on a never ending quest to save my girlfriend...