Some great games you could give a shot include Sega Genesis Collection, Steam World Dig, Runner 2 and Ape Escape On the Loose.
The Sega Genesis Collection for PSP (aka Vita) has almost 30 great Genesis and Arcade games (including but not limited to Sonic 1, Sonic 2, Vectorman 1+2, Shinobi 3, Ristar, Golden Axe 1-3 and tons more!). They are great versions of these classic games and run great on Vita (with customization of the games resolution and if you want smoothing on the games or not). Its only 10 bucks and even without the 'Glitch' that recently ended on PSN, you can still put the game on Vita via PS3->Vita Transfer (I had the game on my Vita since December for example

).
SWD and Runner 2 are simply great games; the former is very addicting and can easily absorb you hours of your time (sadly the game is short though

) and the latter has tons of content, a killer soundtrack, and a rock solid frame rate + native res. Both are great buys

(with SWD being...10 bucks I think and Runner 2 being 10 bucks).
Ape Escape was a nice surprise to me, as with the games dual stick controls, one would think the game would be crap on PSP. But no, the PSP version of the original is indeed great

! The controls are very solid (with the D-Pad being the camera aka right stick on Vita), the visuals are a Dreamcast-level upgrade over the PS1 version, and the game has all the content from said PS1 version. I never played this before outside of the PSP version, but if you never played this before, its a wonderful addition to the Vita with its bright visuals, great controls, goofy charm (the monkeys are really funny

), inventive gadgets to use (running around with a holoahoop to killing things is priceless) and the game just being great fun. Its 8 bucks on PSN and is fully compatible with Vita (you can even get it via Vita PSN store

).
Hope these recommendations help Flandy

.