Any recommendations for PS Vita games?

Gravity Rush is great. Persona 4 Golden and all of the Danganronpa series were my favorites on the Vita.

Muramasa Rebirth was also good, though I don't remember much about the story.

Huge Danganronpa fan actually, but I’ve played them all on other systems. I’ve somehow played P3 and P5 without P4, so thats a great recommendation!
- I would recommend Zero Escape: Virtue's Last Reward. I played that on my Vita back in the day and thought it was great! It has a similar puzzle narrative like Danganronpa but I would say it's more escape room puzzle like.

Tearaway was designed from the ground up to be played on the Vita and I'd say it does a pretty fantastic job of using that hardware well. It's also super cute.

Tearaway is a great game to sink your teeth into to figure out what the vita is capable of. Sadly nobody ever takes it as far as that or beyond so it's downhill from then on for unique experiences. Kinda like nintendo land on wii u. Showcases the huge potential of the system that nobody ever follows up on.

Multiplayer games? Freedom wars, soul sacrifice delta, toukiden, various warriors games (e.g. dynasty warriors, samurai warriors, pirate warriors, etc), Darius burst, Spelunky, dragon's crown,

My favorite single player games are: muramasha rebirth, odin sphere, tearaway, persona 4 golden, rogue ace, luftrausers, rogue legacy, steam world, binding of Isaac. Vita has a strong collection of indie games.

The vita can be unlocked to run homebrew/emulator, overclock,and to use SD card instead of the pricey Sony proprietary card. Check out https://vita.hacks.guide if you want to learn more. People also ported various games not released on vita such as GTA San Andreas, Bully, etc. check out https://github.com/MuxaJlbl4/Awesome-PlayStation-Vita and https://www.gamebrew.org/wiki/List_of_Vita_homebrew_games for more.

I would NEVER buy a vita just to unlock it and play the Tales of Innocence English Patch. Idk what you're talking about, piracy is illegal!!!1 And what sort of loser drunkenly impulse purchases a video game system on eBay because they want to play one game?

edit: if you are reading this, you definitely shouldn't buy an SD2Vita card for a dollar on AliExpress, which is like 1/10th the price of Amazon and the exact same product. Just like you should never engage in piracy!

Uncharted Golden Abyss
LittleBigPlanet Vita or PSP
Tearaway
Killzone Mercenary or Resistance Burning Skies
persona 4 goldens or persona 3 portable
metal gear solid hd or peace walker
Assassins Creed III Liberation
Any of the PS2 rereleases like Ratchet and Clank, Sly Cooper and God or War (Jak and Daxter was buggy apparently)
[INSERT INDI GAME FROM 2010-2018 HERE] Retro City Rampage, Guacamelee, Curse of the Moon, Shantae Half Genie Hero, Stealth In, Steam World Dig, Spelunky, etc.

PSP Games

Star Wars Battlefront Renegade or Elite Squadron
Killzone Liberation
Resistance Retribution
PSP God or War
Ratchet and Clank Size Matters
Ghostbusters
Assassins Creed Bloodlines
Star Wars Lethal Alliance
GTA Vice/Liberty City Stories
PataPon 1-3

Modded Vita

GTA SAN Andreas
Fallout 2 CE
Spyro 1-3 PS1

Additional recommendations

PixelJunk Monsters Deluxe/Ultimate HD
Wipeout 2048
Axiom Verge
Sound Shapes

Definitely give Wipeout 2048 a try. It's easily the best in the series imo and really feels like a proper evolution of F-Zero GX. It's a shame it was never ported to consoles because it would look amazing on a big screen in HD.

What?

It DID get ported to other consoles, it's on PS4 and is called WipEout Omega.

And it is amazing.
- You just blew my mind I had no idea. I need this now

Check out the Ys series on PSP and Vita, they are some of the best games I've played through on my Vita. Digitalemelas.com has a lot of really good info on it.

Also obligatory Persona 4 Golden

I see Ys mentioned a lot! I'm a casual JRPG fan (played Persona 3, 5, maybe half the Tales games, maybe 3-4 FF games, Xenoblade trilogy, Bravely Default + both sequels, 2 or 3 Dragon Quest games, and probably a handful of others). Anything in particular that you'd compare Ys with? And do you recommend I play it in any specific order? I skimmed the site and it looks like they're all connected, although not in order, which makes me think of MGS.
- I’m just getting started with Ys myself having just finished I&II and moving to Origins. I’m playing on a Steam Deck and using this site to determine my play order.
  
  So far I’m getting the impression that this series is going to be kind of like Zelda, but instead of exploration, puzzles and gizmos, you get storytelling, combat and magical items. There are probably much better comparisons to other popular franchises, but this is just what popped into my head as of starting Origins last night.

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.

IMO, the Vita is the best platform for playing Hotline Miami.

Try Soul Sacrifice Delta if you are into dark games.

If you are into action RPGs, check out Odin Sphere.

Also, a good chunk of the PS1 and PSP libraries are compatible with the Vita, so it's worth trying out some classics. I still boot up my Vita once in a while just to play Symphony of the Night.

I picked up one the other week for similar reasons to you, and apart from the other suggestions you've received I would recommend:

Olli Olli - quick to play skateboarding game
Helldivers - still find MP games
Grim Fandango - get it for the soundtrack

Gravity Rush.

It's available on PS4, too, but the Vita remains the definite system to play it on due to how the gyro controls work one to one with moving the screen for controlling gravity.

lol thanks haha, would’ve never thought of that one ;)
I wonder if it will ever get a PC port, and if it would work like that under Steam Deck?
- It could. Gravity Rush 2 is rumoured to be hitting PC.
  
  And there's been progress on Vita emulation.

My son got my vita for his birthday and I have to say tearaway is really one of the best games which rally takes all the features of the vita and blends it into a very creative and fun game.

If I had a Vita, I'd play Silent Hill Book of Memories. I heard it's a really bad game, but as a Silent Hill fan, I'd still like to try it as it is exclusive to that console.

Also, Metal Gear Solid 2 & 3 on a handheld sound pretty cool

Everyone else’s suggestions are better for you, but don’t forget to give Killzone a go. Not as much of a story, but a technical showcase for the system. Also, Uncharted.

Touch My Katamari, Lumines Electronic Symphony & Wipeout 2048 were my most played games on my Vita. It was better suited for titles like that than story ones IMO.

Zero Escape: VLR was great if you like VNs, so was Zero Escape: ZTD. Danganronpa, same deal. Gravity Rush was fun.

The problem with the Vita is that almost everything good on it has been ported out to other platforms. So while it had a bunch of great exclusives during its lifetime, there isn’t much that hasn’t been remade or ported at this point.

Holy shit there’s a Katamari Vita game?! That was my childhood!!!

Go acquire a copy of Persona 4 Golden and we'll see you in 3-6 weeks. Play it blind the first time, save guides or heavy save scumming experimentation for NG+

Edit: I may or may not own a vita purely for P4G 🤫

I assume you've modded your vita, if so both Final Fantasy Tactics and Tactics Ogre are great PSP games to play as well.

Guacamelee! great side scrolling game platform with a decent story https://en.m.wikipedia.org/wiki/Guacamelee!

Time Spinner is available on other platforms, but I enjoy playing it on the Vita