I'd second (or third, or whatever we are up to) considering PS Plus for the vita. My vita got a whole new life once I signed up.
One of the free games included is Gravity Rush which a few others have mentioned. A great little game I feel. Makes good use of some of the Vita's features.
Assassin's Creed 3: Liberation - if you like/play the other Assassin's Creed games, this one is a no-brainer. It's a solid game in its own right, that will make you forget you are playing on a handheld.
Lumines: Electronic Symphony looks fun, but I'm hanging out for it to be available free on PS Plus, which by some accounts will happen in 2 days!
I also just grabbed WipEout 2048 for free via PS Plus, but I haven't played it yet.