I concur with the Metal Gear series. Just because people say that it is overrated absolutely does not mean the games aren't any good.

Dang it, everybody else took all the good ones. My favorite exclusive so far is Ni No Kuni. Absolutely incredible game.

You have to start with Uncharted and TLOU, though. PS3 at its finest.

hmm but do I really want to start at its finest? I might end up disappointed with the rest of the games after. Maybe I should ease into it some?

Hmmm, yeah good call. Maybe save the best for last (or later)? You have plenty of suggestions in this thread, at least, and you won't be hurting for games to play. 

Congrats, btw! Now get to it!  

uncharted god of war ratchet and clank motorstrom tlou tales of etc

Demons Souls!!!

MGS 4 or the MGS Collection with all of the games

also if you like japanese games you should try some of this ones

- Tales of Graces F, Symphonia Collection, Xillia 1, 2 and Zestiria

- Disgaea 3, 4 and or D2

- Yakuza 4 and 5 (which is coming out this year)

- Valkyria Chronicles

- Guilty Gear Xrd

- Dragons Crown

- Nino Kuni

(there are much more of course so feel free to do some searching, you might find something you really like)

Eww, I would not touch a PS3 fat with a ten foot poll after playing on my super quiet super slim. :D

Original PS3 and 360 (especially 360) were both to loud.

I highly recommend Demon's Souls and Ni No Kuni

I've been meaning to pick up a PS3 myself, it's currently still more appealing to me than PS4. Probably because I'm more of a JRPG kind of guy,

Speaking of which, I hear Ni No Kuni and Folklore are really good.

Congratulations, PS3 has lots, lots of games and besides TLOU (don't forget the DLC Left Behind which is as good as TLOU) and Uncharted:

- Infamous, all 2 games + DLC are GREAT, better than Second Son IMO
- Gran turismo 5 or 6 (which is better) are still the reference
- The ICO & Shadow of the colossus collection (beware, you'll want to buy a PS4 next year to play The Last Guardian to play more stuff from Fumito Ueda if you play those 2 games)
- Get the Metal gear HD collection and play all games you never played before Phantom pain that'll release on PS3 too.
- God of War 3
- Pupeeter, a hidden and relatively recently released gem
- You can try Heavy Rain, it's a special experience.

Some Indies-ish, not really exclusive, are incredibly good
- Braid, Limbo, Fez

Also Portal 2 and The Orange Box (Half-life 2 and episodes) if never played before on PC or X360

Finally you can consider subscribing PS+ for all PS3, vita and PS4 games. you'll be happy to have those games if you buy a Vita and or PS4 later.

My favorites on the ps3. Uncharted series, tlou, killzone series, infamous, demons souls, heavy rain, little big planets series, and resistance series. Overall, that's 15 great games.