tammerwhisk: Ya'll generally seem to have a better appreciation for games in general (rather than blind platform fanboyism) so I thought I might as well ask here rather than bother making accounts somewhere else.
Only doing PC (and Nintendo) I'm sure I've missed quite a few console and or ps3 exclusive 'must-haves', but there are too many damn games to simply go through the entire list title by title.
If you don't mind a good thriller style story experience check out Heavy Rain. There's both an original version and a Directors Cut, but the gameplay ending changes depending on your actions. It may have a lot of action sequence style of gameplay, but man it's an intense game at parts.
There's also Beyond Two Souls which was made I think by the same people. It is one of the best looking games on PS3 and really pushes it's graphical limits. The story is quite moving though jumpy (goes back and forth through the timeline), and also plays by action sequences (press a button at the right moment).
If your into JRPG's I'd check out any of the Atelier games on PS3;
Atelier Rorona
Atelier Totori
Atelier Meruru
Atelier Ayesha
Atelier Escha & Logi
Atelier Shallie,
Another coming coming next year
There's also:
Tales of Graces f
Tales of Xillia
Tales of Xillia 2
Tales of Symphonia Chronicles (re-release of older titles)
Tales of Zestiria (both PS3 and PS4)
Tales of Berseria may be both PS3 and PS4 as well next year
Also:
Valkyria Chronicles
Resonance of Fate
A bunch of anime style fighters
Also, one of the launch games back in 2006, Folklore, is quite unique and is quite enjoyable. Plays like an action RPG
Also:
Heavenly Sword
Killzone Trilogy Collection
Resistence Trilogy Collection
God of War Saga Collection
Uncharted
Uncharted 2
Uncharted 3
Ratchet & Clank Collection
inFAMOUS Collection
Drakengard 3
Journey Collection
Disgea 3
Disgea 4
Disgea D2
Steins; Gate (more of a visual novel)
The Neptunia series
If you ever want more recommendations, I spend a lot of free time on occasion staying on top of what's out in the past and now on many systems