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!"

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