Here is an overview of add-ons I consider essential to any web developer or designer who uses Firefox.
ColorZilla
Have you ever seen a really nice colour on a website and thought “That is exactly what I need”. This add-on allows you to get the details about the colour.

Firebug
Websites can be very annoying to code (especially if you use notepad), this excellent add-on for Firefox allows you to edit, debug and monitor code on a web page. It’s so useful it almost needs its own post.
YSlow (For Firebug)
Ever wondered why a website is being slow? This cute little add-on (made by Yahoo) analyses a web page and tells you (in simple English) how to make it load a little faster.

Normally when I use this, I notice a big improvement in rankings on Google and Yahoo.
MeasureIt
Sometimes (especially when coding websites) it’s important to know the size of various elements. Essentially this is like an on-screen ruler.

Web Developer Toolbar
An essential add-on for all web masters (and power users). This useful little tool bar adds everything a web master really needs to keep on top of a website.
Google Gears
I hate JavaScript; luckily the geniuses down at Google seem to know how I feel. Google Gears makes time consuming JavaScript run at least 40%* faster.
Tamper Data
View and Modify HTTP/HTTPS headers, very useful when analysing a web page and working with CURL.

* Based on my benchmarking. Performance may vary from user to user. In general Google Gears is fantastic and should be used on all computers.