There are so many firefox extensions out there already, and every time I think to look at the list there are 100s more, many of which sound pretty cool.
I use (on this PC at work)
BugMeNot - allows me to automagically login to sites like New York Times using a login someone else made and submitted to the BugMeNot database
Copy Plain Text - lets me copy text from a web page without the formatting
Linkchecker - checks a page and highlights bad links
Copy Image - lets me copy images directly to the clipboard
Antipagination - takes news storiies that are broken up into multiple pages and smooshes them all into one page
Adblock - blocks ads
Adblock Updater - downloads new ad profiles automatically. I rarely see ads.
Greasemonkey - a multi-extension which you can add various scripts into to do different things - awesome.
Google Send To Phone - send a text message from the browser. even lets you highlight text and send that
Blogger Web Comments - lets you see what bloggers are saying about a page
DownThemAll! - quick downloads of groups of files
I also have a few web nerd specific extensions:
DOM Inspector
Aardvark - lets you remove elements from a page and see what it would look like, as well as other things (this doesn't work with the newest firefox yet)
HTML validator - what it sounds like
Lynx Viewer - shows what a page would look like in Lynx (or to screen reader software)
You can find all of these at this page. Which ones do you use?