If you like RPG/Adventure games, you'll love the following:
Monster Hunter Freedom 1 & 2 (Hundreds of hours of gameplay from each)
Daxter
Ratchet and Clank: Size Matters
Gurumin: A Monstrous Adventure (one of my favorites and very overlooked)
Brave Story
Secret Agent Clank
Death Jr. I and II
The Legend of Heroes series (though not everyone will like it, I love it though).
There are tons of other great PSP games out, but they are in different genres. I personally own about 78 games right now (almost owned around 120, but I ended up selling about 35 games on ebay and made close to $600). If you need anymore recommendations in other genres, I have plenty
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