For me:
- The DanganRonpa games are absolutely essential. At least 1 & 2. Fantastic high school murder-mystery with compelling characters and plot.
- Steins;Gate has rapidly become one of my favourite Vita games. Just a beautiful story, world and soundtrack and well worth experiencing.
- The Atelier Arland games, particularly Totori and Meruru, feel like they were built for the Vita in mind and look absolutely gorgeous on the OLED screen and are perfect to play in bits and pieces on the go.
- WipEout 2048 is almost the definitive WipEout game thanks to HD/Fury being included as DLC. It's well worth picking up Pure & Pulse too thanks to their small file sizes.
- Tearaway is an experience well worth having and is honestly the only Vita game where I feel it gets all the Vita's features right (i.e. camera, back touch etc.)
- Hotline Miami 1 & 2, again, feel right at home on Vita thanks to pick up & play nature. Banging soundtracks too.
- Geometry Wars 3 and Super Stardust Delta, both perfect twin-stick shooters that really show off the Vita's dual analogues, and really pop on the handheld's screen.
- I'm not a massive fan of 2D artsy platformers, but I found Teslagrad to be an absorbing experience on Vita, helped by the fact that clearly a lot of love and care went into optimizing it for the platform.
- Ys: Memories of Celceta isn't the best Ys game, but it's well worth experiencing if you like ARPG's. Tales of Hearts R gets a shout out too.
Honestly I love my Vita, and there's many more games than this that I'd recommend, but they're the must have titles that'll never leave my library.