A must! Web development plugin. Inspect the site structure and experiment with the code while seeing the changes applied directly in your page. Great for bug fixing and cross-browser checking / adjustments.
FTP Client inside of Firefox. Very handy indeed. Although I mostly use eXtplorer to upload files, it's very handy to have this tool inside of Firefox itself.
Web Developer Toolbar
Adds a menu and a toolbar with variuos web developer tools. I use the function for highlighting DIVs all the time (creates a red line around the div the mouse hovers over). Hugely time saving!
Track where your site ranks in Google, Yahoo and Microsoft Live Search using this free Firefox addon.
Draw out a ruler to get the pixel width and height of any element on a webpage.
Saves a webpage as an image. You can save or copy either the whole page, the visible portion or a selection. Great for documentation.
Enables you to use the embedded IE engine within Mozilla/Firefox. Show the page as it will look in IE in a separate tab.
View Source Chart
View page source with HTML Chart GUI.
If you know of other useful Firefox plugins for Joomla users, please comment!