I guess the best PSP game out today is Final Fantasy Dissdia. Its 39.99 but I say 40$. It has all the action you need almost easy to understand right away and controls are simple once you get the hang of it and there is about 60+ hours of gameplay. I have so i highly reccommend it.
Hope this helps = )

Try one of the monster hunter freedom series,
monster hunter freedom is the first one
monster hunter freedom 2 is the sequel to monster hunter freedom which has new monsters and items
monster hunter freedom unite is the latest having more monsters and overall more gameplay time.
I would strongly recommend one of these games, i have them all and together i have collected 1034 hours gameplay time, its just so addictive, also if your friends have it you can link up and do quests to slay beasts together.
Hope this helps!

” Gran Turismo ”
Release date: October 1, 2009
Best PSP Game in E3 2009

Tekken Dark Ressurection
GTA Liberty City Stories or Vice City Stories
NFS Underground Rivals

Dissidia Final Fantasy. .