This is a list of the Extensions that I've found most useful for Firefox. Most of them can be accessed through the “Get more extensions” link on the Firefox Extension panel.

Adblock - Lets you easily block ads from certain sites

BBCode - Adds context menus for formatting stuff using BBcode, HTML, etc.

Bookmarks Synchronizer - Allows you to upload bookmarks to a web or ftp server and synchronize another machine with that file.

Copy Plain Text - Copies text without the formatting (for pasting into emails and such)

Downthemall - Download all the images on a page (or linked from a page) en masse. Could also be used for other file types, I suppose.

Flashblock - Replaces embedded Flash with a button that you can click to turn on the flash (I got tired of noisy Flash adds)

Forecastfox - Weather Forecasts embedded in the browser

IE View - Loads the current page in IE, for those odd cases where something won't work in Firefox.

Image Zoom - Allows you to zoom and fit images

Linkification - Surrounds plain text URLs with anchor tags.

MiniT - Allows you to drag-rearrange tabs.

Mozilla Archive Format - Allows you to save web pages as a single-file .mhtml archive, similar to internet explorer's. (Grab this from maf.mozdev.org instead of the regular extension page, as that one is out of date.)

MR Tech About - Puts some useful stuff in the Help menu.

MR Tech Local Install - Various things to help install themes and
Extensions. (Sorting of installed Extensions by name, install extensions from disk, turning off the time delay, etc.)

No Script - Lets you choose which sites are allowed to use Javascript.

Nuke Anything - Lets you temporarily remove a specific object from a web page.

Outfoxed - A useful Social Network thingy. Lets you rate pages as you browse, and lets you also see ratings of your informers (your friends, and others you trust, ideally). Check out the Nutshell overview on the site for details.

PDF Download - Lets you decide whether to save a PDF or display it in a new tab (as PDF or HTML). This is helpful if you accidentally click on one because large PDFs tend to freeze the browser while they download and render.

QuicktabPref Toggle - I use this to get access to certain options (like forcing other applications to open links in a tab), not for the toggle feature.

Sage - RSS aggregator, used to view updates to sites like mine.

Smiley Xtra - A database of emoticons, categorized, in case you dislike the ones on a particular forum.

Tabbrowser Prefs - Puts a new entry in the Preferences for Tabbed Browsing

Tab X - Adds a close button to tabs. I have the TabX-Ultra version that leaves the main toolbar's “close tab” button intact.

Text zoom - Allows you to enlarge or reduce the text on a site. This extension is not configured correctly for recent Firefox installs, but it can be made to work with some trivial editing.

Tinyurl Creator - Makes tinyurl much faster, since it makes one and copies it to the clipboard.

HTML Validator - Probably not useful to anyone but web page developers. It checks the HTML of the pages you browse to make sure it is valid. Beware … this tends to screw up form buttons on some sites (like Google)

MediaPlayerconnectivity - This does nifty things to videos and such embedded in web pages. Such as let you view them in a standalone browser of your choice. I find it useful to avoid being stuck with a certain player size on gamespot and such.

EditCSS - another one for people who write web pages. This lets you alter the CSS of the site on the fly, so you can see what effect certain changes will have.