1. Web Developer
This is the daddy of Firefox plug-ins, it lets you do so much and saves so much time. It would take me forever to go through the full list of features but I'll just highlight the main ones that I use in my role as a Technical SEO.
Document Outline - This will show me the logical heading structure on a page. So you'd expect a h1 at the top, then a h2 or h2s inside the h2s should be h3s and so on. If any headings are out of hierarchy it shows them up here.
Display Image Alt - Nice and simple this one just overlays all of the alt attributes on its relative image. handy for finding images that have no alt on them.
Re-size - Great for web design, this lets you re-size your browser window to any size you select. Good for testing out your site on smaller resolutions.
There is also an option to edit CSS but I prefer the editing facilities in FireBug shown below
Firebug is amazing for web designers and developers. It can do many things like analysing page load times, which also shows you what elements are slowing you down. HTTP Header responses, show you your DOM information. The main power of this comes in the HTML and CSS tabs, for instance right click on anything and hit Inspect Element will bring up that element in a code window under the web-page. You can now directly edit and manipulate that page to test and make changes. It will not be live for the world to see though just locally for you to modify a page until on-the-fly you get the right look. This is a brilliant feature for web developers as it saves editing saving and refreshing.
This is a simple very small plug-in that I miss when it isn't there. It places a small box in the status bar and displays the IP address of the current site. Right clicking on it gives me access to whois and some dnsstuff tools taking you straight to the page with the information about that IP address.
I use it mainly for using an IP:000.000.000.000 searches to check for sites that exist on that IP address.
4. Server Spy
Another very simple plug in is ServerSpy, all this does is tells me the server type and version that the site has been served up using. Right clicking can give you extended information.
If you want any of these plugins head over to https://addons.mozilla.org/en-US/firefox
and tap in the titles I have put above.