I have been developing websites for about 5 years now and I have come across some of the neatest Firefox extensions ever made. By that I mean I use them every single day. If you've even gone to Firefox's Recommended Add-ons page, you'll find some plug-ins that you wont ever use. What's this?? They're recommended!! Yes, but that doesn't mean you'll use any of them. Their list of recommended add-ons includes things like MAP+, ChatZilla, Cooliris, Weather, eBay, and auto-blog-posters. All of these things are cool and useful, except for helping with web development.
Alas! da404lewzer's list of Great Firefox Extensions All Developers Need!
Web Developer 1.1.4
This handy tool allows you to take full control of your website's css, form, source and misc. information. It is a MUST HAVE for anyone doing websites or at the very least, myspace designs.
Html Validator 0.8.4.0
This handy validator will inform you if your page is w3c compliant without having to submit it. It shows all warnings and errors and can be configured to use TINY and SGML parser.
This is simply the liquid crack of the interclick. Once you have an account specified with tags, you'll be given a new site related to those tags each time you click Stumble! You will learn more and more every day with this.
IE Tab 220.127.116.1170528
This extension allows you to use the Internet Explorer engine directly inside Firefox. This is great for ensuring the page will look good in both browsers. Click the FF logo in the status bar to switch to IE and back.
This handy tool is great for when clients give you links to pictures to use as content. This will save everything, mostly time!
Mouse Gestures 1.5.2
This will shave seconds by not having to go all the way to the top of the browser to click back or use backspace. You might actually get something productive done today because of it.
Yoono is very cool because it shows you lists of sites similar to the one you are on. This is very handy when trying to find other sites in the same category. When your client says, "have you heard of digg.com?" You can reply, "of course, have YOU checked out slashdot, delicious, reddit, engadget, technorati, lifehacker, boing boing, wired, fark.. etc etc?"
I hope that these help you out. If there are any I missed I will add them. Please leave me comments as to what your favorite Firefox Extensions are and what you use them for!