Another good topic for our beloved X Box. As a proud owner, I'll be more than happy to give everyone my take on it:
1.) The Elder Scrolls IV: Oblivion- Easily one of the most immersive experiences I've ever encountered. Just look at some of the most epic series in gaming:
-Zelda, Final Fanatsy, Mario, etc.
NONE of the above games have the level of immersion as Oblivion. You can literally, talk to ANYONE in the game, traverse the map ad nauseam, and basically do whatever you please. To me, it's the only RPG that seems "real". This is why I never considered Fable a true masterpiece. Granted it was a great game, but the Elder Scrolls series simply revolutioized X Box RPGs.
2.) Kotor- I commonly refer to this game as Star Wars D&D. What's so amazing about the game is that it revolves around human choice. Your quests, ending, etc. can be completely different depending upon which path you choose. Like oblivion, another thing that made the game a winner was supplementary sidequests. Simply put (for me at least) this is the best Star Wars game ever made.
3.) Halo: I've always believed that the series itself was overrated, but you really can't argue that the multiplayer was Brilliant. Stop for a second in retrospect: What value was place upon multiplayer back then? I believe the answer to that question is "very little". Since the success of Halo came to light, Microsoft (ad other companies as well) have come to see the potential of communal gaming. Granted, there was online gaming far before Halo came out, but it singlehandedly changed the perception and priorities of developers (especially within the realm of shooters)
I really think those games stand out above all thus far, so I'll just throw out some final notables:
Beyond Good and Evil: As many people know, this is one of my favorite platformers of all time. Go buy it, now! (it's multiplatform)
Gears of War: It was a really cool game, with excellent graphics and multiplayer, but it was just too damn short.
Expect to add to this list in the future, because Microsoft has some KILLER games coming out. Keep your eyes open.