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Rondo of Blood and/or Symphony of the Night

If you have custom firmware they will work just fine, just extract the files you download with Winrar or something and put them into the ISO folder on your PSP.

Initial D soundtrack

Puzzle Agent 1&2

A ton of Sakura games on HumbleBundle, no regrets...

Do you have custom firmware on your PSP?

The Defenders from Netflix

Now that I have found this thread, here's every game I've beaten this year:
Battlefield 3 (2011)
Battlefield 4 (2013)
Batman: Arkham Asylum (2009)
Batman: Arkham City (2011)
Black (2006) ...