My top 5 in order are:
1. Steins;Gate
2. Persona 4 Golden
3. Danganronpa: Trigger Happy Havoc
4. Gravity Rush
5. Danganronpa 2: Goodbye Despair

Hey John you know if you can find yourself a Vita with firmware version 3.6 or lower it is possible to get homebrew on it, if it would interest you I've been having a blast with Mame on my Vita the last couple of weeks reliving the days of the arcade glory on the lovely OLED screen, guess that is my recommendation lol! every arcade game ever now on the Vita!

Lots of great games mentioned already, I'll add a few that have not made it into others posts.
- Earth Defense Force 2017 Portable
- Earth Defense Force 2: Invaders From Planet Space
- Soul Sacrifice (better than Delta imo)
- Killzone: Mercenary....ridiculous. Must have. Get the physical if possible. Big file for digital
- Final Horizon. Playing this one right now.
- Hot Shots Golf: World Invitational. A fun, pick up game until it becomes the poster child for rage quitting. Great with buddies though. The campaign gets mental quick, and the online community is full of sharks.
- Do you like MGS 2&3? Get them in the HD collection.
- Hyperdimension Neptunia: Action Unleashed. A straightforward beat em' up with fun, breezy dialogue. A good one to play in bursts if you need something engaging, but not difficult.
I could go on, and on, but those are a few not yet mentioned.

Too many to name from the top of my head but many here have listed the majority of what I was thinking? Are the memory cards still expensive in retail stores? I hear they are a bit cheaper through international sellers. I've always played my friend's Vita but never got my own because of the ridiculous pricing of the cards.

I was able to swallow the insanity of the card prices....But I totally get that others can't, even just on principal. It's gross. I literally had a clerk at the checkout wonder if the cost of 32gb of memory was a pricing error. I had to explain to him that it was just way it was with the Vita. Then I made the "duuuhhh" sound and smelled my fingers. Repeatedly.

Digimon Story Cyber Sleuth

Persona 4 golden, I'm not sure if Persona 3 is available on vita but if it is get it as well.

Only just realised Project Diva X was out. Ordered from Play Asia (US Vers) because its digital only here -_-

Only one other person mentioned it so far, but I'm gonna suggest Soul Sacrifice.

I dumped maybe 70+ hours into that game, and the story is really engrossing if you're paying attention to it.

And the multiplayer was pretty fun. I don't even enjoy multiplayer games, but I spent a lot of time in it with that game. Highly recommend.

Nice, I won't be able to get it since I don't have a Vita D: