Since we've got a new thread I'll list all the ones I use. Looking at this list, I'm amazed FF still runs quite happily, but it's fine with all this lot installed:
1-Click YouTube Video Download - Adds some simple buttons for quickly grabbing videos. There are similar, more complex addons about but I like this ones simplicity.
A Bit Better RTM - If you use the very good
Remember The Milk then this adds some nice functionality. Also available as a Greasemonkey script.
Adblock Plus - Essential. That's all there is to say.
Add Bookmark Here ² - Another tiny but very handy addon. Allows easier bookmarking, apparently Apple stylee.
All-in-One Sidebar - Another essential one for me.
BBCode - Indispensable if you post a lot on forums such as this one.
British English Dictionary - Like it says, gives a British angle to the spellchecker.
Clear Cache Button - No explanation required, I use the button in the All In One Sidebar.
ColorZilla - Allows easy picking of colors from anywhere on a page; very handy for web-development, graphics work, etc.
Easy DragToGo - I mainly use this for swipe saving images to a certain folder without having to go through any menus. There are other addons that do this differently but I've used this one for ages.
Evernote Web Clipper - Very handy if you're an
Evernote user.
FaviconizeTab - Love this one; really useful if there's a load of tabs that you always have open and you want to save tab-bar space.
Firebug - Like Dave says, incredibly useful addon if you're doing any web-development.
FoxyProxy Standard - Allows fast switching of proxies with the ability to filter certain urls to proxies, etc. Great in conjunction with
Tor.
Greasemonkey - Like Paul says. Opens up a vast array of website customisation scripts. Extremely useful.
LastPass Password Manager -
Lastpass is an awesome password manager. This addon interacts with it very well. Until recently I used a handful of passwords for everything. I've now redeemed myself and use randomly generated 13 digit passwords. Obviously these are impossible to remember but Lastpass makes it easy. Beef up your security, Lastpass is free.
Link Gopher - Rarely used, but it does it's job well - extracts links from a page and spits them out into a new tab for easy further processing, for example in the Rapidshare Downloader.
NoScript - Like Slack--Line says. Awesome addon, especially for blocking popups, popunders, etc. Now on my essential addon list.
RDown - Rapidshare Downloader - You can feed this addon a load of Rapidshare links, go away and when you come back there's a good chance it will have grabbed them all for you.
ScrapBook - Archive pages or parts of pages. Gets most use here for recipes that I've found online, cooked and want to file for later use.
Screengrab - Selective screen grabs; not used often but it works well.
Session Manager - Like butterworthtom says. Another essential one for me - very powerful tab management and recovery.
SortPlaces - Bookmark sorter.
Taboo - Another essential - great tab-saver for when you find a page you don't really want to bookmark, but will probably want to come back to later.
UrlbarExt - Adds some very handy features to the URL bar.
Xmarks Sync - Will probably be surpassed by native FF features but in the meantime a great way of syncing bookmarks (and passwords if you so wish) between multiple computers.
