There are all kinds of really cool homebrews available for the PSP (assuming you have a homebrew-capable firmware). These ten are a selection of the ones I think are the most exciting, with the most interesting or useful possibilities.
The links lead to external sites where you can download the programs. Please note that homebrew is not supported by Sony, and installing homebrews on your PSP may void your warranty.
WiFi Sniffer is a tool to let you use your PSP to find nearby WiFi networks and monitor their status. If you're away from your home network, you'll be able to easily find open networks where you can use your PSP online. Unfortunately, this homebrew (as with many others) works only with version 1.50 firmware.
Turn your PSP into a universal remote using this homebrew and the PSP's infrared port. Again, this homebrew only works with firmware 1.50, but if you've got the right firmware, this is a very cool application to play with.
PeP Viewer is designed especially to help you read manga (Japanese comics) on your PSP. It has an adjustable scroll function, zoom, rotate, and more. Anything that lets me read more comics has to be good.
Find out what the weather conditions are by inputting your country and/or zip code with this nice little app. There are versions available for firmware 1.0 and 1.50.
AFKIM is an instant messenger program for PSP. It's "almost universal" in that it handles AIM, ICQ, MSN, GTalk, and Yahoo! instant messaging. So, likes its name says, if you're away from your keyboard, you can still instant message with your PSP. The other nice thing is, it seems to work with version 2.0 firmware.
PSpoof is a useful program that lets you use the PSP's Photo Sharing function to send any file (under 2 MB) from your PSP's Memory Stick to another PSP. It works by attaching a valid jpeg file to the file you want to send.
Psp-httpd lets your turn your PSP into a portabe web server, allowing your to browse your PSP's files wirelessly from your computer, cellphone, or other wireless-enabled device. You can even host a website on your PSP if you want to. This homebrew works with version 1.50 firmware.
PortableVNC (Virtual Networked Computing) is a program that lets you use your PSP to control things that run on your PC, using the PSP's WiFi connection.
PSPRadio is a music player for PSP, but it's more than just an MP3 player (though it does that, too). With PSPRadio, you can access online streaming music, using the WiFi capabilities of the PSP.
Okay, so I had to throw one silly program in here, but who wouldn't want to turn their pricey, shiny PSP into an Etch-a-Sketch? Come on, try it; it'll be fun.