Bavarian: A few recommendations from my favourite genre, Hack and Slash Action Adventures:
God of War series
Even the PS2 and PSP titles are available on PS3 as HD Collections.
Bayonetta
A little bit overrated imo, and the PS3 version is a really bad port. But definitely a must-have-played.
Dante's Inferno
Doesn't stand out as much as the above mentioned titles, but it's a more than solid game. And if you like the genre as much as I do, you will have your fun with it.
El Shaddai - Ascension of the Metatron
Requires tolerance for its Japanese artsy-fartsy nature. Look it up on YouTube and decide for yourself if you like that style.
As for Action Adventures that are more on the adventurous side, besides the already mentioned ICO and SotC, I can recommend Majin and the forsaken Kingdom. A sorely overlooked gem.
Shooters:
Condemned series
Part 1 is also available on PC. Part 2 is console exclusive. Excellent games.
Shadows of the Damned
Japanese (meaning: absurd) content meets western gameplay mechanics. Gotta love it.
And last but not least:
Vanquish
If you're a 'shooter with gamepad skeptic', this one will cure you. The story is dull and not worth talking about, but the gameplay is so outstandingly good and satisfying. A prime example for perfect controlls.
personally speaking I thought Bayonetta was rubbish but it certainly was unique. One day we will get Vanquish on pc. *sigh*