The following games are compatible with any legal firmware 2.x or newer, and do not require any hacking of any kind (they are safe HTML-based games that run through the PSP built-in Browser).
To install a game: download the corresponding file, extract it to a new folder on your computer (Windows only), launch the Setup, and then follow the on-screen instructions. The installer will automatically detect your PSP, and install the game on it (it will simply copy the game files to the memory card, and then add an entry to the bookmarks so that you can play the game from the Internet Browser of the PSP).
There are also PC/iPod/iPhone games but who cares PSP is the bestest
There is also a PSP Game Maker
Post your homebrew finds and remember to keep it legal nobody like a thief.
Hopefully this will be stickied so there is no excuse for "There are no free games for PSP"