For exclusives, it depends on your taste; I'll list a few:
1. Uncharted: Drake's Fortune - 3rd Person Action Shooter - I highly recommend this one. Smooth animation, excellent graphics and gameplay, a good story, and plenty of unlockables to play around with if you enjoy those things. It's currently my favorite game of this console generation.
2. Lair - This is a flight action game. If you enjoy games like this (Rogue Squadron, Star Fox, etc.), it's worth a try.
3. Heavenly Sword - Action - This one is really short, but really fun. Lots of flashy combos and special techniques, as well as an enjoyable story with great graphics and voice acting. It's certainly worth a playthrough, but once you beat it, there isn't much left to do except play it on a harder difficulty.
4. Folklore - Action RPG - I haven't gotten too far in this one, but so far it's an enjoyable (yet linear) action RPG. Reminds me of the Lost Kingdoms series for the Gamecube.
5. Disgaea 3 - Strategy RPG - I haven't played this at all, but it received good reviews.
6. Resistance: Fall of Man - FPS - This game is fairly good with an interesting style of graphics; I don't care for it too much, though, to be fair, I'm not really impressed with any of this generation's FPS contributions (unless you count the Orange Box)
7. Resistance 2 - FPS - A sequel to the previous game. I haven't played it.
Edit: Forgot a couple.
8. Ratchet & Clank: Tools of Destruction - Action platformer - This one is really fun. Gameplay-wise, it's got excellent controls with a good variety of weapons to unleash on your enemies. The graphics are vibrant and colorful, with a lot going on the background, and it has a good amount of unlockable content to play around with.
9. Ninja Gaiden: Sigma - Action - This one barely counts as an exclusive. It's another remake of the Ninja Gaiden game from the original Xbox. It has an amazing combat system, but an irritating camera and quite a few cheap fights on the harder difficulties (which you unlock one by one for completing the game). If you enjoy a challenge, this is a good choice.