Playworthy Games
Tony Hawk's Underground 2: Remix
Hot Shots Golf: Open Tee (Just bought the 2nd)
Star Wars Battlefront 2 (First PSP game, played for days straight)
Final Fantasy Tactics: War of The Lions (Only $20 now at Best Buy)
Grand Theft Auto: Liberty City Stories
SOCOM: U.S. Navy Seals Fireteam Bravo (Or any SOCOM game)
Wipeout Pure (Good racing game for $15)
NBA 08/09 (Gotta love Basketball Video Games)
Madden 08 (Gotta love Football Video Games)
God of War: Chains of Olympus (I've played it and it probably kicks donkey)
Lumines (Love it, very addictive and PLENTY of replay value)
Crisis Core: Final Fantasy 7 (Just started playing it, love it. - A MUST for any FF7 fan)
Ratchet and Clank: Size Matters (Graphics are great, several high tech and interesting weapons. I love R&C)
Castlevania: Dracula X Chronicles (The original game is o/k, but the real beauty is the unlockable Symphony of the Night PS1 game. If you haven't played it then this is a good opportunity)
Burnout Legends (Great graphics, fun mini games. Good racing game)
Metal Slug Anthologies (Awesome run and gun side scrolling shooter game!)
Some others could be like
Metal Gear Solid: Portable Ops (It was ok for me, but a lot of other people love this game)
Killzone: Liberation (I Haven't really played in depth only about 30 mins but I didn't care for the camera scheme and controls.
There you have it, these are 15+ games that I guarantee will keep you busy for a while.