If you like mecha and read japanese (or don't mind fumbling through it's Japanese)... Super Robot Wars. It's an awesome and addictive series. Much more fun if you can read Japanese though. The stories and conversations are a big part of the game, because otherwise the game mechanic is super simple.
Any of the Disgaea games, hilarious, difficult, and very fun. (PSP 1+2 / PSVITA 3+4)
Final Fantasy Tactics War of the Lions is great, sadly never finished it though (PSP)
Hyperdevotion Noire Goddess Black Heart SRPG spinoff of the Hyperdimension Neptunia series, and it really makes for a great game the in game chibi models are pretty bad though, but I personally don't like the chibi aesthetic often(PSVITA)