I seem to have a lot of extensions that I like, but here are a few ones that I probably can't live without (well kind of...):

Adblock- I use it to block out all the adds that bother me!
Bugmenot- Used to sign into sites that require to sign up before continuing
Performancing- Used for blogging.
Gmail Skins- Used to customize the Gmail interface (and you get extra features such as smileys).
Minimize To tray- So that I can minimize firefox without closing it
User Agent Switcher- To get access sites that require IE even though they support Firefox.
Sage- I use this for all my RSS needs. And I use the hicks style (instead of using the Safari style)
Chatzilla- To chat...
Google Toolbar- To check page ranks and especially to check my spelling!
Gmail Notifier- To know about how many new emails I have...
Reveal/Showcase/Foxpose- For something like expose...
Web developer- To check CSS and to see if pages have errors
Image Zoom- To zoom into images
Site Advisor- To keep me free of spyware, spam, viruses and phishing (or online scams)
Tab mix plus- To help me manage my tabs.

And finally I like my Firefox search plug in that I created (which is sort of like an extension) to search SysChat and a few search plug ins to search other sites and a few Greasemonkey scripts.