Valkyria Chronicles is one of my favorite games this generation, check out the demo and see if you're interested. I'm sure you can find it cheap.

You should totally get inFamous and inFamous 2, plus Uncharted 1. I will post more suggestions as I think of more.

EDIT: you may also like:God of War 3/ God of War Collection, Heavy Rain, flower(PSN), The Resistance games, Yakuza Games, Killzone 2 and 3, MAG Motorstorm games and GT5 if you're into racing, 3D Dot Game heroes if you like Zelda

EDIT 2: I found a lot of interesting sounding PSN games: inFamous: Festival of Blood, Rochard, Rocketbird: Hardboiled Chicken, Tales of Monkey Island, Back to the Future, Pixeljunk Games, PAIN, Under Siege, Lead and Gold, Calling All Cars, Everyday Shooter, so many that I'm too lazy to put them all

Infamous games > Personally I liked the second much more than the first, but that seems far from a universal opinion.

Little Big Planet games > Only played the first, but if it's new to you I reckon the second is a better pick-up, since user made levels from the first are playable with the second.

Possibly Heavy Rain? Not for everyone I guess, but I had a good time with it, it's different anyway. Best to check out some footage if you have doubts.

Also the first Uncharted is a very good game. I'd play that before 2+3, I believe it has aged well...

I bought a PS3 just to play Heavy Rain but that's probably cause I'm a sucker for art games^^

Still is a unique experience that i would recomend. Other games to consider would be the Uncharted, Infamous and God of War games.

I don't really care for God of War but i think the first Uncharted still is a good game even thou it's not as awesome as the sequel :)

God Of War 3, God Of War Collection and God Of War Origins.

Trash Panic from the PSN store. Honestly, so fucking good.

I couldn't even fathom buying a console so late in the cycle. I mean, there's so many games.

• Uncharted Drake's Fortune (it's still a pretty great game, hampered by probably the worst combat of the series - 3 gave it a run for its money in that regard, though.)
  
• Heavy Rain
• Motorstorm Pacific Rift
• God of War 3
• Resistance 3 (don't bother with the first two)
• Flower
• Killzone 2 (3 is probably not worth purchasing)
• LittleBigPlanet 2
• Rochard
• Infamous 1, 2 & Festival of Blood
• ICO & Shadow of the Colossus HD Collection
• Ratchet & Clank Future: A Crack in Time (Tools of Destruction is also fun)
• Wipeout HD Fury
• The Pixeljunk series is worth a look at
• Joe Danger (although it's probably worth waiting for the XBLA version now)
  

Skyrim.

Disgaea 4

Really there are a ton of PS3 only titles, it depends a lot on your taste.

Valkyria Chronicles, Flower, Pixel Junk Eden (try the demo) and Motorstorm Pacific Rift.

Wipeout HD + Fury expansion <3

Metal Gear Solid 4. I mean... duh? Anyone who owns a PS3 and doesn't own MGS4 is a disgrace to gamers. No, a disgrace to mankind. Nope. A disgrace to all intelligent beings that have ever existed!

Okay, just kidding ^^ Still my personal favorite of the exclusives, but only worth it if you're into the MGS universe and if you've already played the previous entries.

What I'd definitely recommend to anyone with a PS3 is the Uncharted series. Uncharted 1 and 2 are pretty much independent, with 2 being vastly improved in many areas.

And the Ratchet and Clank games are pretty awesome and original.