Not counting homebrew games, the PSP currently only plays games on UMDs (Universal Media Discs) and official digital downloads. With the right homebrew, the PSP can emulate many different consoles and play their appropriate ROMs.
Aside from movie and music videos available commercially on UMD, the PSP can also play video files from the Memory Stick. These files must be in MP4 or AVI format.
Music can come on UMD (though usually it comes in the form of music videos). You can also load up your own music to play, as long as it's in one of the formats listed (you may not be able to play some of the file formats if you're using a Memory Stick Pro Duo, though; only the Memory Stick Duo is compatible with all file formats).
Photo & Image:
- jpeg (aka jpg)
Anything that comes on a UMD can be played on a PSP, images included. Images don't have to be photos, either; any image files saved in a compatible can be viewed on the PlayStation Portable.
Different firmware versions are compatible with different file formats. The more recent the version you have, the more file formats you'll be able to view. Use the tutorial linked below to find out which version of the firmware you have, then check the firmware profiles to find out more about file compatibility