Firefox is an insanely good web browser; I've fully integrated tabbed browsing into my web surfing, and I love the customizability and easy privacy / security configuration. I even badgered the tech people at work into installing Firefox on my office and lab computers (IE is the only browser they normally install).
However, I only recently started exploring the extensions that are available for Firefox. Extensions are small bits of code that extend the functionality of Firefox; they're completely free (I think they're open source), and are written by users of the browser. Features like extensions are what make open-source software so powerful: any user who thinks, "Hmm, this could be done better," can dive into the code, make it better, and then share the improvement with the entire community.
Here's the extensions I've found to be useful:
Single Window - Forces links that would otherwise open in a new window to open in a new tab (preventing one of the most annoying trends in web design).
Define Word - When a word is highlighted on a page, this extension provides a link (on the right-click menu) to look up the word using your choice of dictionary pages.
Tabbrowser Preferences - Creates a "tabbed browsing" area in the preferences window, which adds many options to control the behavior of tabbed browsing (including forcing searches started with the search bar to appear in new tabs in the background).
MediaPlayerConnectivity - Redirects streaming media to other media players, so you can play the streaming media in your media player of choice (outside the browser). Very useful for Linux, which lacks good plugins for streaming media.
Security / privacy
CookieCuller - adds more cookie editing abilities; it allows you to "protect" some cookies so that they are not deleted by the "remove all cookies" option (or the "keep cookies until I close Firefox" option), which makes removing unwanted cookies much easier.
View Cookies - lets you view the cookies the current page is setting.
SwitchProxy Tool - Adds a menu to the browser's status bar allowing you easily switch between multiple proxies. Convenient if you have something like Privoxy or Tor installed (both of which I'll be writing about next week).
SecurePassword Generator - Creates randomly generated passwords, but doesn't store them (you have to remember them).
Gmail Notifier - Adds a little notifier to the bottom of the Firefox window that reports how many unread messages you have in your Gmail inbox. An editors pick, and I can see why: after only a few days I'm already relying on it to tell when I have new Gmail. My only gripe is that it doesn't check multiple accounts.
Bookmarks Synchronizer - A utility that allows you to synchronize your bookmarks across multiple computers, by storing them in an FTP account of your choice.
Sage - An Atom and RSS feed aggregator built into Firefox. I'm still waffling between just reading blogs by checking everyone's page (using a bookmark toolbar folder which I "open in tabs" every morning) and using an aggregator; we'll see if Sage tips the balance.
[Update Dec. 2005: I've stopped using Sage, and have switched to Liferea, an open-source feed reader for Linux/Unix. I've also stopped using the Gmail Notifier (I had it set to check for new mail frequently, and gmail got mad at me), and have started using the Session Saver extension.]