The Vita is my favorite handheld of all time. I say this as someone who owned every Nintendo handheld since the original Game Boy.
If you have a PS4 they make for fantastic companion hardware and indeed bring a lot more value to PS Plus and cross-buy/save software.
Haters gonna hate, but IMO it's the wealth of indies that make the system great. Indies are cheap and the experiences many of them offer are perfect for portable gaming. Of course, the niche Japanese games are another draw for me. Especially if you like DRPGs, a languishing genre. But you get awesome stuff like EDF 2017 & 2 as well. If you skipped the PSP or PS1 you have a huge legacy of inexpensive software to work through on a far better piece of hardware than the PSP.
This is also the first, best (and probably last) handheld for fighting game fans. I mean, the fighting game ports are just as good as their console brethren for gameplay (assuming you aren't lost without an arcade stick) thanks to the specs, screen and dpad. They have pretty good online! That is integral. Handheld fighters on older consoles were worthless without a friend with their own system and copy. Games like Street Fighter x Tekken and Skullgirls even have cross-play with console players. Ports like The Last Blade 2 are arcade-perfect (it's actually superior to the PS4 port). I feel like this is a huge plus for the Vita that is often ignored.
I mean, just look at this list:
Ultimate Marvel vs Capcom 3
Street Fighter x Tekken
Injustice (on sale right now for $5, big story mode)
Skullgirls 2nd Encore (cross-buy)
Dengeki Bunko: Fighting Climax
The Blazblue Series
Arcana Heart 3 Love Max
Dead or Alive 5 Plus
The Last Blade 2 (cross-buy)
Mortal Kombat 9 (PSA: online for this title is disabled now)
Guilty Gear XX Accent Core+ R (PSA never had online)
...Do Dive Kick and Nidhogg count?
Um. Don't buy Playstation All Stars...
Also, big props to its fantastic battery in sleep mode. My 3DS dies seemingly overnight in sleep, the Vita will stay alive all week. And it automatically downloads updates!
As a PS Plus user you should make sure to use the cloud saves. For some dumb reason deleting a Vita game deletes the save, too. You're gonna wish you had sprung for the 64gb card soon...
I keep hearing this, but I've heard it's not really a game. That's not a deal breaker to me if it's like a Japanese take on Telltale or something, is that what it is?
It's a game in the same way Phoenix Wright is a game. I got it on sale for $13 on PSN. I like it but I'm glad I didn't pay more.
If you like good indie games you should get:
Downwell
Rogue Legacy
La Mulana ex
Axiom Verge
Binding of Isaac
Nuclear Throne
Super Meat Boy
Luftrausers
+
Resogun
Geometry Wars 3
Good list. Allow me to add:
Severed
Guacamelee!
Risk of Rain
Crypt of the Necrodancer
Fez
No Heroes Allowed: No Puzzles Either
Hotline Miami
Mutant Blobs Attack
The Swapper
Frozen Synapse Prime
Spelunky
OlliOlli 1&2
Velocity 2x
TxK
Big Sky Infinite
Joe Danger
Sine Mora
Pixel Junk games
More (less obvious) Recommendations:
Disgaea 4
Lumines - Amazing rhythm puzzler!
Rayman Origins and Legends - probably the best Vita platformers
Need For Speed Most Wanted - acceptable port of fantastic open world racer
Sonic All-Star Racing Transformed - the Vita's only logical answer to Mario Kart
WipeOut 2048 - the Vita's F-Zero!
Hot Shots Golf: World Invitational - the only Golf game you need!
The Pinball Arcade - free table! Cross-buy tables!
Zen Pinball - free table! Cross-buy tables! But really, pinball is awesome and these are awesome games
Metal Gear Solid HD collection - good 30 fps ports
Sly Cooper collection - good ports
Sly Cooper: thieves in time
God of War Collection - okay, these aren't great ports but they are a good deal on sale
Dungeon Travelers 2 - awful pervert stigma aside, possibly the best oldschool DRPG on Vita
Monster Monpiece - again, gross pervert angle but surprisingly fun lane-battle card game
The EDF games - it's portable EDF!
Don't buy Senran Kagura games. They're... Not very good.
Of course, people will tell you to buy Killzone Mercenary but I personally find that shooters just don't feel good to play on the Vita. KZ:M is an excellently made game, though, and your best option for the genre.
I will also champion P4G, Digimon Cyber Sleuth, FFX/X2 and Soul Sacrifice Delta.
Cheap, good PSP recommendations:
Patapon 2
Castlevania Dracula X Chronicles
Gladiator Begins
Z.H.P.
Final Fantasy Tactics: War of the Lions
Tactics Ogre: Let Us Cling Together
God of War: Ghost of Sparta
Half Minute Hero
Brandish: The Dark Revenant
Persona 3 Portable
Disgaea: Afternoon of Darkness
Puzzle Quest
Pursuit Force: Extreme Justice
Pac-Man: Championship Edition (PS Mini)
Peggle (Mini)
Tetris (Mini)