Okay, guess what folks? I done went and bought myself a new PSP. So I guess I'll get this thread up and running again. And if you find an app that you think should be on this list, PM me about it. If I like it, I'll +rep you, and give you some points (How's 10,000 sound?) if vbPlaza ever gets reactivated.
And now, down to business.

ADDED:
FuSa GamePad v.2 Andy_maN's FuSa GamePad. Transform your PSP into a functional Gamepad for PC gaming (Windows or Mac).

FuSa SD 1.0.50 OldPrisoneR & Andy_maN's PRX plugin enabling TV out with any cable on the PSP Slim — component, composite, s-video, d-terminal, etc...

UPDATED:
Bookr-Mod 20090709 A modified & enhanced version of Nguyen Chi Tam's Bookr for viewing PDF, TXT, PalmDoc, DJVU, and HTML documents on your PSP.

Hold+ 4.0
A prx for conserving battery life when the the PSP is in "Hold mode"

Netfront Internet Browser - HighMemMod Beta 4 Ardatan's Netfront Internet Browser uses the HighMemoryMod by Team P86 to remove browser memory limitations. Use all 64MB on the PSP Slim and 32MB on the PSP Fat. This is currently beta.

PSPTool 1.00 Raing3’s homebrew app that allows you to backup & restore the IdStorage, inject or dump memory stick IPLs, convert from/to a normal/service mode (Pandora) battery, and more.

Ultimate PSPTube 2.0 - HighMemMod Alpha 2 Ardatan's High Memory Mod release of Ultimate PSPTube version 2.0.

And, as always, everything can also be found on the front page.
Enjoy, and if you use something, a simple thanks or +rep is always appreciated.