I see so much multiplat games on those list, so here, for me, the best exclusives games for the 360:
Last Odyssey (JRPG, I really dont like it to much, the story for me is really boring)
Infinite Underscovery (Action Rpg, is like xenoblade on wii or white knight chronicles on ps3, I didnt play it too much but a far I played was some what enjoyable)
Tales of Vesperia (JRPG, another really good tales of game, one of my favs tales games)
Magna Carta 2 (Action Rpg, at the time was came out was ok for the grapphics but now, well I dont think so. I got bored when I replayed again)
The witcher 2 (action rpg, if you love action rpg you will love this one, if not you will hated it because the story is kinda boring)
Fable 2 (for me this equal good to the first one)
Alan Wake (excellent "horror" game, is like a silent hill game that you need to resolve puzzle and find stuff, as well survive againts the enemies but not like a shooter. I said "horror" in this way because for me was more drama on the story than horror)
Gears of war 1 (for me the best one of the series, third person shooter)
Bio shock (This was a exclusive tittle for 360 but now you can find it on ps3, first person shooter)
Ninety-nine nights (if you like dysnasty warriors you love this too)