http://kotaku.com/the-12-best-games-for-the-playstation-3-5877932
I don't really mind violence, so I'm just going to go ahead and recommend it: try the hell out of Red Dead Redemption. It's open world, a great story, and murder your heart and offer you a chance to do something about it.
Kingdoms of Amalur: Reckoning was a favorite of mine, although I recognize it as an unfinished product (I believe it was originally intended as an MMORPG). Some might find it unoriginal or bland, but I found it beautiful and the story enthralling. The only thing I really hated about it was the storage system.
I also recommend Dragon's Dogma. And...I'm just going to say the words "Dark Souls." I'm...not going to be an asshole. But..."Dark Souls."
Oh yeah, if you get ANY Bethesda game, make sure you get their GOTY editions. But, yeah, Skyrim and Fallout are super-fun.
While they're violent, they're not COD type of violent, I recommend checking out "Resistance: Fall of Man" and "Rage."
And Minecraft. Apparently, apparently Minecraft.