Final Fantasy Tactics. I have never played another game with a storyline as deep and complicated as that game. The plot is so good that you can take away the entire game aspect, and the story would still be worth experiencing.
Unfortunately, it was kind of a side-project of Square so it didn't get the development it should've. Antiquated, sprite-based graphics and shoddy translation/localization can really work against it. I hear the PSP version is very cleaned up, but that the story was simplified. Either way, if you like strategy RPGs and you want a good story full of betrayal, murder, conspiracy, manipulation, and warfare, all without an awkward forced love interest, look no further than FFT.
Deus Ex is another masterpiece of storytelling mixed with gameplay. If you like FPSes with RPG elements, this is the game for you (downloadable from Steam for $10 or so.)
Edit: It's worth mentioning that both games have amazing musical scores. For proof, Deus Ex was composed by the same company who did the original Unreal Tournament.