For arcadey racing, you can't go past Need for Speed: Most Wanted. Especially if you have friends with a PS3 as well. Just good fun trying to beat each other's scores/times.
I'd recommend Journey, downloaded from the PSN Store. Great game.
Also recommend FIFA 13, if you want to see Aston Villa have any kind of success.
Edit:
Oh, and also the God of War series if you're into action-adventure hack-n-slash stuff. God of War 1 and 2 are available in an HD collection (both were originally published for the PS2) and God of War 3 was released on PS3. The new one - God of War Ascension is due out March.