1. Greasemonkey
Greasemonkey allows users to install scripts that make on-the-fly
changes to specific web pages. Greasemonkey can be used for adding new
functionality to web pages, fixing rendering bugs, combining data from
multiple webpages, and numerous other purposes.

2. Firebug
With Firebug you can edit, debug, and monitor CSS, HTML, and JavaScript live in any web page. Works with: Firefox: 1.5 – 2.0.0.*

3. Web Developer
Web Developer extension adds a menu and a toolbar with various web developer tools. Works with: Firefox: 1.5 – 2.0.0.*


4. Html Validator
HTML Validator is a Mozilla extension that adds HTML validation inside
Firefox and Mozilla. The number of errors of a HTML page is seen on the
form of an icon in the status bar when browsing. Works with: Firefox:
1.5 – 2.0.0.*

5. JavaScript Debugger
JavaScript
Debugger provides a powerful JavaScript debugging environment for
Mozilla based browsers. Works with Firefox: 0.9 – 3.0a1

6. MeasureIt
With Measureit you can measure the height and width properties of page
elements by drawing a ruler. Works with Firefox: 1.0 – 2.0.0.*

7. Poster
A developer tool for interacting with web services and other web resources
that lets you make HTTP requests, set the entity body, and content
type. This allows you to interact with web services and inspect the
results. Works with Firefox: 1.5 – 2.0.0.*

8. CSSViewer
With this extension you can view CSS properties of page elements. Works with Firefox: 1.5 – 2.0.0.*

9. Load Time Analyzer
The Load Time Analyzer allows developers
to measure and graph how long web pages take to load in Firefox. Load
Time Analyzer produces graphs that show the occurrence of events such
as requests for the page, images, stylesheets and scripts, along with
events like the execution of an onload script. Works with Firefox: 1.5
– 2.0.0.*

10. FireFTP
FireFTP is a free, secure, cross-platform FTP client for Mozilla
Firefox. It also includes more advanced features such as directory
comparison, syncing directories while navigating, SSL encryption,
search/filtering, integrity checks, remote editing, drag & drop,
file hashing etc.. Works with: Firefox: 1.5 – 2.0.0.*

11. FirePHP
Visualize and control your PHP backend from Firefox. FirePHP allows you
to take a deeper look at all the work your PHP code does to generate
that page you are currently looking at in your Firefox browser.

Update:
12. ColorZilla
With ColorZilla you can get a color reading from any point in your
browser, quickly adjust this color and paste it into another program.
You can Zoom the page you are viewing and measure distances between any
two points on the page. The built-in palette browser allows choosing
colors from pre-defined color sets and saving the most used colors in
custom palettes.

13. X-Ray
Once installed the X-Ray command is available by right-clicking as well
as in the Tools menu. When applied to a page it can help you see how
the document was constructed without having to go back and forth
between the sourcecode and the page in your browser. Is that list made
of li, dd or p elements? Is that an h3 tag or just some bolded text?
X-Ray shows you what’s beneath the surface of the page. Works with
Firefox: 1.5 – 2.0.0.* [Thanks Andy]

14. Aardvark
Aardvark allows you to clean up unwanted banners and surrounding
“fluff,” especially prior to printing a page. See how the page is
created, block by block. View the source code of one or more elements [Thanks Manu]

If your favorite extension is missing from the list, drop me a line i will add it to the list.