For those with 6.20 and above who want homebrew...

http://wololo.net/wagic/ :thumbup:

This is the ONLY cost-free, Pandora Battery-free, Magic Memory-free way I know of to work around firmware. AFAIK, none of these exploits can damage your PSP, and do not modify the firmware in any way. Please note that you WILL need to write files to your memory stick in some way, regardless of which firmware you have.

Personally, I have used Half-Byte Loader for all sorts of great homebrew, including Duke Nukem 3D, Cave Story, and Jelly Car.

EDIT: Installing HEN on top of Half-Byte Loader does four things.
1. When you boot up Half-Byte Loader as you normally would, you will be returned to the main menu after a few seconds. "Memory leakage" is normal to see, don't be alarmed by it.
2. The HBL menu is unreachable from here on, but you won't need it.
3. More homebrew games and applications are now usable after you run Half-Byte Loader!
4. All compatible homebrew games and applications should work as game demos or downloaded games do UNTIL YOU RESTART YOUR PSP. Then you will need to run Half-Byte Loader again.

The main reason for installing HEN in the first place is the ability to switch between normal PSP functions and homebrew-type-stuff.

IMPORTANT NOTE: You WILL need the Everybody's Sukkiri demo for most of the homebrew enablers, and you can get it off www.pspdemocenter.com (or the PSP store if you have the latest OFFICIAL firmware).