I don't have too many indispensible applications. Antivirus Guardian and Spybot Seek & Destroy to keep my PC safe.
I recently switched to Opera after Firefox started getting weird on me. It was about time, though. FF is too high-profile now, and the black hats have started exploiting it. (Is there a decent FTP plug-in for Opera? I haven't needed it yet, but I'm sure I will soon.)
Illustrator, Photoshop, Premiere, and After Effects for school (and mapping. Well, the latter two not so much—I'm not an expansimator).
Sony Acid Pro and a little piece of audio editing shareware called N-Track Studio, which is nearly as good as Soundforge but 1/5 the price tag.
QuickGamma to keep my monitor calibrated. DeepBurner for CD/DVD burning. Winamp for media playing.
The Font Thing is a recent addition, but one that I think I will continue to use. I keep my old CorelDraw disc handy for the fonts folder and license.
For web editing, I use Notepad. And I make frequent use of the Windows Character Map, though I am getting better at remembering keystroke commands for special characters that I use frequently.
Shareaza for downloading The Big Bang Theory, since CBS continues to refuse to put it up on their website for online viewing.