Seconding Soul Sacrifice Delta. Great Monster Hunter-ish game, but much more accessible and interesting world and lore.

Some I haven't seen yet in this thread: Shinobido 2. Great ninja stealth game in the vein of Tenchu (same developer), really love this one. You sort of play an evolving mission based campaign with three major factions. You can choose which faction you want to do missions for, and the outcome of the overall story is impacted by who you choose to work with.

Gundam Breaker 3 (though it runs a little poorly if you don't have the overclock patch). Amazing they got this to run on a Vita at all, really. Hopefully Breaker 4 dethrones it, but this is still the best Breaker game to date.

Gundam Extreme Vs Battle. Really tight competitive Gundam game. No customization here, more about fighting with the famous Gundam of the series, plays really well and satisfyingly.

Grand Kingdom: real fun and unique action RPG. Combat happens turn based, but you execute your combos in real time and can juggle enemies and such, hard to explain this one, but I really like it and it's a shame it never got a port or sequel somewhere.

Killzone Mercenary with Botzone DLC: the best shooter that got made for the Vita. Still looks impressive, plays pretty well!

Dragon's Crown: it's Diablo as a beat em up, what more can I say? At the same time every other Vanillaware game on Vita, but Dragon's Crown is my personal favorite for on the go.