There are all sorts of really cool homebrews available for the PlayStation Portable, assuming you have a homebrew-friendly firmware installed. Here's a selection of interesting games and programs.
The graphics, audio, music, and menu in Silveredge are polished and impressive. You jump right into the game and the controls are explained as part of the gameplay. This space-shooter homebrew game feels very much like you are playing a commercial game.
PSPokemon Grey is a fan-made homebrew that brings Pokémon to the PSP. Interact with trainers and others to collect your pocket monsters.
Turn your PSP into a digital Etch-A-Sketch with PSP Magic. Relive your childhood with this homebrew version of the classic game. Use it for your own imaginative creations to save and share with others.