I don't know what of these games have been mentioned, but I love my Vita and either me or my wife play it daily.
First off, get a PS+ subscription. More than half of the games I have for the Vita and PS3 have come from it and on the Vita side they've been mostly great. Also, find a cheap(er) 32 or 64 GB memory card on Ebay (or Amazon if you're more comfortable with it), you'll be glad you did. Also, if you don't need a game right now and it isn't on PS+, there's sales on at least a few games all the time, with additional discounts for PS+ members.
Also, I highly recommend spending 10 bucks on handle grips that make it feel like you're holding a controller, it's much more comfortable. Move up to 20-25 and there's grips with a battery pack in them for extra battery life.
You definitely want to play Dangonronpa 1 and 2 before the third one, and while the third is a bit of a departure it's definitely worth it too.
Muramasa Rebirth and Dragon's Crown - You can play Muramasa on the Wii, and DC on the PS3, but both those games absolutely shine on the Vita, and the screen makes them look gorgeous. If you aren't at all into 2D brawling you might want to look at a video to be sure.
Soul Sacrifice Delta - I put over 100 hours into the original, and will approach that number again with Delta. I can't get into Monster Hunter, but this game takes a darker aesthetic and cuts right to the meat of 4-players tearing down a gigantic beast with booming attacks and gigantic HP bars. Just as playable in single-player.
LittleBigPlanet - I don't like any of the LBP games on PS3. The touchscreen interface and other Vita "gimmicks" and level design/story on this entry though make it a game I really enjoy, and the level editor is a snap to use. Playing other people's creations changes entire genres at times and it's great.
Gravity Rush - If you're into open-world games with lite RPG elements, this one is a must. Cute and endearing protagonist, interesting city, and very different controls that actually work. I've had more fun with it than any Assassin's Creed game.
Disgaea 3 and 4 - You already know I'm sure if you're into Disgaea, but if not it's a quirky and delightful series of very strategy based JRPGs that feel right at home on the Vita. Vita versions include all extras and DLC from PS3 and more crammed onto the little screen.
Tearaway - It's a platformer, and it's easy, but it really is an absolutely magical game in a world of paper that uses almost every aspect of the Vita system.
Persona 4 Golden - The definitive version of one of the greatest JRPGs ever made. You can have Persona 1-4 on the Vita, but 1 and 2 may be too rooted in old-school design philosophies these days.
Ys: Memories of Celceta - A perfectly fine starting point to jump into the Ys series, and an absolutely fantastic action-JRPG in its own right.
If you like FPS games at all, Killzone: Mercenary is the greatest and best looking incarnation of an FPS game on a handheld. Period. Unless you really love FPS games, though, the novelty of how amazing the technological feat is wears off when there's better FPS games on the big platforms.
Sword Art Online - Depends on your opinion of the anime, and the idea of playing a "VRMMO" (you aren't online with others, it's simulated), but there's hundreds of hours of game here that includes an HD remake of the PSP original as well. The translation is pretty bad though.
If you're into fighting games, the ports of Mortal Kombat and Injustice are butter smooth with only a graphical downgrade, but you can't play online anymore. Blazblue, Street Fighter X Tekken, and Ultimate Marvel vs. Capcom 3 are perfectly suitable replacements, but I gravitate to Mortal Kombat personally.
The Binding of Isaac: Rebirth is an amazing thing to be able to pull out at any time and do a run.
You have the ability to play Final Fantasy 1-X-2 at any time.
If you're into Terraria and/or Minecraft, the Vita is the best way to play those games portably aside from carrying a laptop with you.
If you like shooters/shmups (I'm a freak for them), there's Geometry Wars 3, Velocity Ultra/2X, Resogun, Sine Mora, Pixeljunk Shooter, TxK (Vita exclusive spiritual sequel to Tempest 2000), Luftrausers, and Gunslugs.
A list of games from other systems that I prefer to play on the Vita due to portability and/or how great the screen looks: Spelunky, Rayman Origins, Guacamelee!, OlliOlli 1 & 2, Hotline Miami 1 & 2 (these are so much better with the touchscreen), Rogue Legacy, Steins;Gate (VN, but might be one of the best stories in any medium), Grim Fandango, Bit Trip Runner 2, Child of Light, Lone Survivor (great at night in bed with headphones), and La-Mulana EX.
Those are just the games I own, I wouldn't mind picking up the MGS HD collection, Sly collection, RE Revelations 2, Tales of Hearts R, Lost Dimension, Hyperdimension Neptunia, or Toukiden:Kiwami if they ever go on sale or are PS+ games. The only game I paid full price for was Borderlands 2, and I'm not sure if I regret it. The graphics are extremely downgraded and the framerate is permanently at 15-20 fps, but it's the whole shebang with 6 characters and 2 DLC areas. I got used to it, then I played remote play on my friends PS4 and his Handsome Collection version and it was no fucking contest at that point, and it's hard to go back. Oh yeah, that's another thing! If you ever get a PS4, you get the ability to play portable Dragon Age 3, Bloodborne, Dark Souls 2, and pretty much whatever the hell else is on PS4. I can't wait to be able to do that and let my wife have the TV.
But yeah, shame they didn't make any games for the damned Vita...