Homebrew is noncommercial software. Emulators are a good example.
Nesterj: a damn good NES emulator -
MAXCONSOLE - Playstation Portable - NesterJ PSP v1.20 released - NES emulator for PSP
PSPGenesis: name says everything -
http://files.psp-homebrew.eu/PSPGenesis-v1.18c.zip
Okay, "other programs"
UMDDumper: Rips a UMD. With the m33 firmware installed, you can throw the image this thing makes into a directory labeled "ISO" on your memcard and play the game straight from the card. Also good for ISO archiving.
Popsloader is a set of programs that will let you rip a PSOne disc to a playable PSP game image. Because of what needs to be found and done, I'll let you do the walking