I second both LBP and Demon's Souls (Quite polar opposites, aren't they?).
I also had a lot of fun with Heavy Rain, though it's definitely not for everyone. I came in with no expectations and ended up getting really attached to the story & characters, despite it being completely out of my normal game comfort zone.
Don't put it at the top of your list, but it's a nice little gem of a game if you do get around to it.