Originally posted by Dr. Cossack I'll let someone else take care of recommandations. :)
Here I am.
LittleBigPlanet or 2 seem to be the definitive game to get for the system. It's just one of those games that everyone who owns a PS3 gets. Like Mario with Nintendo. You can snag the first LBP for pretty cheap, even the GOTY Edition version (which includes pre-downloaded content you would otherwise need to pay for ala DLC), and it's a pretty solid game. Once you're done with it, if you liked it and decide to get the sequel, all of the stuff you got from the first game will carry over to the second one, like one big expansion pack. Unfortunately, stuff from the second game isn't backwards compatible with the first.
If you're curious, you can always download demos of games through the Playstation Store for free. At least that way, you can get a hands on feel of these games.
Games I own full versions of that I'd recommend: LittleBigPlanet 1/2, Modnation Racers, Infamous, BioShock 1/2, Resident Evil 5, Castle Crashers (Download title), any Call of Duty game (Modern Warfare 2 namely).
Games I don't own, but are highly revered by other PS3 owners: Uncharted 1/2, Bayonetta, Heavy Rain, Killzone 2/3, probably others I'm missing.