If you can find a copy of Hexyz Force I would recommend it. Bought on PSN for $3.50 and its awesome. Also like others have said Persona 3 is a must.
Others I like are: Flatout Head on, Gran Turismo, Race Driver 2006, and Persona 2.
PSN: extremeM
PlayStation Vita Japanese Software Sales (Media Create Physical/ Famitsu Digital)