One of the most useful features of Firefox is its open, extensible plugin architecture, which allows major customizations to its behavior. With every new release of Firefox, many extensions break simply because they are not permitted to install. Other times, something critical is actually changed. Finally, sometimes a new version provides functionality that you formerly needed an extension for. This is my current list of extensions that I'm using on the brand new Firefox 2.0; it replaces a quite similar page that talked about extensions I used with Firefox 1.5. Some of the items on the list have changed, some are still the same. Several things have vanished, a couple new things have come along. In fact, this list itself has changed over time.
Aardvark is a Firefox extension that permits you to perform a live edit on a webpage prior to printing or saving. Its primary purpose is to permit you to remove elements from the page, but it will also strip color, "de-widthify" (strip the width from the HTML elements) and perform a handful of other functions. It's a nice companion to Scrapbook which will allow you to capture whole pages, or capture a selection, but not to omit chosen elements from a page.
AdBlock Plus is an ad-blocker that actually removes items from web pages. Not only do you not see the ad, but in most cases, you don't even have a hole in the spot from which the ad was removed. Since it's never loaded, no bandwidth is used by the ad, either. Relatively recent versions of this extension do network updates, so you no longer need an additional extension for updates (e.g. AdBlock Filterset.G Updater.)
The All-In-One Sidebar puts a lot of common functionality into a sidebar, instead of pop-up windows. It's most suitable for users with high screen resolution. History, bookmarks, downloads, extensions, themes... I find it to be much more convenient, although you do occasionally find yourself resizing it to get access to some of the buttons.
The BugMeNot extension uses the BugMeNot website, which provides you passwords for websites that have free registration, so you don't have to bother signing up for an account, and provide your personal information. The primary example is the New York Times.
Cookiesafe is an extension which controls which sites are permitted to set cookies. You can specify that all cookies from a host or domain should be accepted, or never accepted; ordinarily you are prompted every time a non-whitelisted site attempts to set a cookie. A convenient menu is provided at the lower right corner of the browser window for rapid access to the function to permit/deny a site.
del.icio.us is a social bookmarking site that allows the use of "free tagging" to categorize your content. Unfortunately their official plugin is marked as not being supported by 2.0. We could make it compatible with the "MR Tech Local Install" or "Nightly Tester Tools" extension, but instead I elected to move to del.icio.us complete which provides a little more functionality. I also use the del.icio.us direc.tor to provide a worthwhile interface to del.icio.us. (See also the greasemonkey script I use to fire it off.)
DownThemAll! (or "DTA") is a download manager that's loaded right into firefox. Somewhere along the line, Firefox seems to have lost its ability to resume downloads; I don't think it even tries any more. DTA not only supports retries, but also all kinds of other neat stuff (like deferred-schedule downloads, and queueing.) FlashGot is broken anyway (it causes memory leaks) so this is far better than using an external download manager.
Gmail File Space (gspace) is a cross-platform extension (Windows, Linux) that allows you to store files in a gmail account, from your browser. Very handy for mobile users, esp. those portable firefox types. Download to the local drive's temp directory, then upload to gmail, and you can pull it out later. We don't all have lots of room on our flash drives. The best part? It looks and acts just like a FTP application with a queue.
Google Browser Sync synchronizes your browser settings to your google account; it both provides crash recovery (returning you to your previously-loaded pages) but also keeps your browser settings synchronized across all computers upon which you use this extension. I formerly used Session Manager which provides the crash recovery, but doesn't synchronize.
The PDF Download extension helps you avoid loading the PDF browser plugin when you don't want it. You can still open files in the browser as normal, but you can also throw them to an external PDF viewer, download them, or view them as HTML.
Scrapbook: Internet explorer has MHT files, which are basically webpages saved as the MIME portion of a MIME email. Firefox, with this extension, has scrapbooks, which is pretty much the same thing as performing a "Save As..." from the File menu, and saving as "Web Page, Complete". Either way, it's a way to easily save a webpage as a single package (in this case, a directory.) Scrapbook has import/export capabilities; you don't need them to copy a scrapbook someplace but they do make it much easier (due to the types of directory names used by Scrapbook) and exporting from one profile and then importing into another preserves metadata like the original URL.
Talkback: This is the extension that sends error reports to the Mozilla foundation. I mention it here simply because if it is installed it will appear in your list unless you explicitly elect to disable it during installation, or later.
If you are developing web pages, you need the Web Developer extension. It can hide or mark various web page items like graphics and so on. It can show you the outlines of tables and their cells. It resizes web browsers to given sizes in order to emulate the effects of having a particular screen resolution. It has menus that change the behavior of cookies, CSS, and a number of other features.
Xinha Here! opens the Xinha WYSIWYG HTML editor on any textarea. It's very handy for websites that allow you to write HTML. I used to use this because I wanted WYSIWYG HTML editing for my own website (this one! not that I need rich HTML editing often) but the plugin provided by Drupal uses TinyMCE which used to produce HTML with no line breaks. Which is bad. These days it doesn't do that, and I mostly use it for other, more random websites.