The original 'Arkham Asylum' is the best of that bunch ^ IMO. But my favourite titles on the PS3 (Excluding AA) have been (In order):

1. Deus Ex: Human Revolution (By a huge margin. Characters you care for, complex story, action, stealth, gorgeous design, it has it all)

2. Red Dead Redemption (GTA on horses. A vast world in meticulous detail)

3. Tomb Raider 2013 (Emotional stuff. Puzzles and stealth in a semi-sandbox. Becoming a crackshot with the bow is just magic)

4. Fallout: New Vegas (You could almost live in this game it's so frickin' massive and involving)

5. Wolfenstein 2009 (Big guns and evil Nazis to kill. It's pure action FPS fun)

Also Sega Mega Drive Ultimate Collection is a great way to get an instant and large collection of oldskool classics for very little. Plus the triple-bundle 'HD Collections' (Metal Gear Solid, Tomb Raider etc) are cost effective packages.

Honourable mention for 'Max Payne 3'. It's by a long way the hardest game I've ever played. It starts off near impossible but becomes more playable later on, after much practice. If you can get past the initial painful difficulty spike, it gets very good indeed.