Considering Getting a PS Vita

[Halazar]

Vta is a great system to own if you like Japanese games in the slightest.

A few suggestions:

Persona series. You can get pretty much the entire series on Vita if you include PS1 classics and PSP games.
Danganronpa 1 and 2
Ys series (Memories of Celecta for Vita. Ys 7 and Oath in Felghana for PSP)
Final Fantasy X HD remaster and FF 7, 8, 9 as PS1 classics
If you like rhythm games you may want to give the Project Diva f games a look
Gravity Rush
Muramasa Rebirth and Dragon's Crown
Tales of Hearts R
Tearaway
Uncharted Golden Abyss
Wipeout 2048
Virtue's Last Reward (If you don't already have on 3DS)
Atelier series (Rorona, Totori, and Meruru and I think Ayesha comes out soon on it)
I don't have much experience with indies but Velocity Ultra and Velocity 2X are both very fun
Classic PS1 RPG's such as Xenogears, Chrono Cross, Suikoden 1 and 2, Legend of Dragoon, Grandia, Breath of Fire 4, Wild Arms 1 and 2
Other classic PS1 games such as Castlevania: Symphony of the Night, Metal Gear Solid, Resident Evil 1-3
The Legend of Heroes: Trails in the Sky for PSP
Honestly there are a lot of PSP games I would recommend but I can't really remeber which are available to download on Vita and which aren't. You may need to look up a list.