Mine:

Firebug
https://addons.mozilla.org/en-US/firefox/addon/1843

Indispensable.

Greasemonkey
https://addons.mozilla.org/en-US/firefox/addon/748

Mainly use this one for the Gmail hacks and custom written hacks.

Live HTTP Headers
https://addons.mozilla.org/en-US/firefox/addon/3829

Useful for debugging

Download Statusbar
https://addons.mozilla.org/en-US/firefox/addon/26

This in minimode should be built into firefox in my opinion.

BugMeNot
http://roachfiend.com/archives/2005/02/07/bugmenot/

Really useful when you can't be bothered to register for a website.

I only really use the Download Statusbar and FasterFox.

FlashGot
https://addons.mozilla.org/en-US/firefox/addon/220

Sends downloads straight to FlashGet

Greasemonkey
https://addons.mozilla.org/en-US/firefox/addon/748

Gmail and Digg hacks mainly

Web Developer
https://addons.mozilla.org/en-US/firefox/addon/60

Helpful when coding

AdBlock Plus
https://addons.mozilla.org/en-US/firefox/addon/1865

Don't criticize me for blocking ads. When you're on dial-up they really do slow you down.

Web Dev Toolbar, Firebug, FireFTP and occasionally "Screen grab!"

ColorZilla, Firebug, Flashblock, IE View, Linkification, MeasureIt, Web Dev Toolbar.

Tab Counter, Adblock, Linkification, Screengrab, Tamperdata, Web Dev, and Autocopy (highlight to copy text)

I was playing with that a while back, trying to modify outgoing post requests from flash, never worked. Had any luck with that?

I use ChatZilla, Download Statusbar, Forecastfox, and VideoDownloader.

i cant live without WEB DEVELOPER & FireBug

I use Ad Block, ColorZilla, Web Developer and some other ones, just those the most. I could probably live without any extensions though. Except maybe Ad Block on certain sites that are very obtrusive.

Status bar, various themes/skins, Foxy Tunes, Ad Block, and... Web Dev.

I don't think I ever tried it with flash, only with my own scripts when I was sorting out a secure paypal ipn script

User agent switcher, add n' edit cookies, colorzilla, seo for firefox, translator with a UK dictionary, adblock plus.

dictionary and del.icio.us buttons..

My collection is quite vast

Colorzilla
Download Status Bar
Gmail Manager
Greasemonkey
HideIP
More Tools
No Script
PasswordMaker
StumbleUpon
TabPreview

and a few others that have been disabled because they are annoying.
I probably could live without a few of them but they just make web surfing so much easier and is why mozilla rules over IE
LONG LIVE FIREFOX!

Also Chatzilla