Once you install the extensions Doug suggested, look into these to give yourself even more browsing power.
For more peaceful web browsing, Adblock will help wipe out all of the annoying ads you encounter while browsing the web. 
Colorzilla makes website development a whole lot easier by allowing easy identification of the color being used in a particular portion of the page.
Adding the Download Statusbar to Firefox allows you to monitor your downloads without opening the download window. 
Firebug is the ultimate Javascript debugging tool.  No web programmer should be without it.
For anybody who browses the web while listening to music, FoxyTunes is essential, allowing most music players to be controlled directly from within Firefox or Thunderbird. 
Google Toolbar (http://toolbar.google.com) puts the search box in a more useful place, and provides a number of useful features including type-ahead suggest. 
Also for web programmers, HTML Validator checks web pages against the W3C standards, and can even fix common errors.
 IE Tab and OperaView use the Internet Explorer and Opera rendering engines to view pages within Firefox, rather than forcing web developers to open those other browsers.
For users with a scroll-wheel mouse, Image Zoom allows you to right-click-and-scroll to make an image larger or smaller.
LinkChecker will verify that the destinations of links within a webpage exist. 
FasterFox provides a friendly interface to a number of behind the scenes tweaks for speeding up browsing.
