Uncharted, first and foremost.

After that, Warhawk, if you like online ala BF2 (though with less emphasis on realism), and Heavenly Sword if like hack n' slash ala God of War and Devil May Cry. Though I must warn you about Heavenly Sword. The game is rather short, so it may be a good idea to rent it first to make sure it's worth a purchase.

And if you like weird RPG-ish action/adventures with beautiful artstyle, I'd definitely recommend Folklore. Definitely download the demo, if nothing else.

Call of Duty 4

Ninja Gaiden Sigma

Uncharted

Ratchet and Clank Future: Tools of Destruction

Warhawk

SuperStardust HD (PSN)

Everyday Shooter (PSN)

Uncharted
Ratchet and Clank
PixelJunk Monsters
Everyday Shooter
Burnout Paradise (since the PS3 version is actually better for once)
Heavenly Sword
MLB 08 The Show

I liked 'Folklore' and 'The Darkness' quite a bit. They're not must-haves, but they're definitely worth picking up used.

'Uncharted' is the only "must-have" PS3 game so far that I can think of and even it can get slightly repetitive.

You should try:
Rathcet & Clank
Heavenly Sword
Call of Duty 4

The only exclusive I really enjoyed enough to buy was Uncharted. Rent Heavenly Sword, it is also quite good but short.

On the multi-plat front, Rock Band (Guitar Hero is this game's bitch), CoD4 (must-have if you love shooters), and Assassin's Creed were very good games released in holiday 07.

As far as exclusives go I would highly recommend Ratchet and Clank Future: Tools of Destruction and Resistance: Fall of Man (the game may be more than a year old already but it is still great and I think it is necessary for the complete experience if you also are going to get Resistance 2 coming out later this year).

As far as non-exclusive games go I would highly recommend Burnout Paradise, Call of Duty 4: Modern Warfare and The Elder Scrolls IV: Oblivion.

Just download demos off the PSN and see what you like, the demos are pretty representative of what the games are like. As for games that I don't recall having demos, get Oblivion and The Orange Box (if you like story-based shooters). The graphics aren't that great but there's just so much play value in both of them. Oblivion is great if your hands hurt from button-mashing and you just want something more leisurely. Also, a lot of the games that don't have an online component can be pretty short (Uncharted, R&C, Heavenly Sword, etc), so you may want to rent them, if you play intently you'll have the games finished before the rental is up.