While Google's Chrome has yet to roll-out the inevitable onslaught of extensions, Firefox has loads ready for the taking - many of which provide great value to both developers and designers. Let's look at a few and why you’d want to use them.
 

Web Developer Toolbar: This very popular extension provides users with the ability to perform site checks and disable certain technologies (like JavaScript) that impact how a site appears in a browser which is helpful during testing. The extension has won the hearts and minds of designers and developers though mostly because of the ability to edit CSS in order to see if an alteration would fix a problem.

YSlow: With over 8,500 downloads each week, YSlow is an immensely popular tool to help developers (and designers) analyze web page load times, letting them know why they are slow based on Yahoo's rules for high performance websites. Those using the extension can see a performance overview, HTTP/HTML summary, a list of components on the page and includes tools such as JSLint.

Server Switcher: An excellent extension for developers, Server Switcher is a navigational help tool. That means users can switch between sites on their development (platform hosting the temporary version you are currently working on) and live servers, so that changes can be immediately seen. I use this tool regularly at home. Features include support for subdirectories (as well as different ports and local files), multiple projects can be created, and the whole app can be launched with a keyboard shortcut.

SQL Injection: With all the fear surrounding SQL attacks the past few months, this extension might help to allay some fears. The component transforms checkboxes, radio buttons, and  select elements in form fields to an input text, providing the ability to disable elements from the forms. This makes it much easier to test and identify SQL injection vulnerabilities.

Bugg.gd Error Search: bug.gd is the global error search engine. Everyone helps grow the database by providing their solutions to unsolved errors they run into. The goal is to ensure that no human ever has to research an error that has already been solved. Simply copy an error message and click a couple of buttons to start searching for a solution - you can't get much easier than that. Drastically reduced the number of network calls required, using the new XML-based bug.gd API.

Firebug 1.2.1: Firebug integrates with Firefox to put a wealth of development tools at your fingertips while you browse. You can edit, debug, and monitor CSS, HTML, and JavaScript live in any web page.

Poster: A developer tool for interacting with web services and other web resources, Poster lets users make HTTP requests, set the entity body, and content type so you can interact with web services and inspect the results. Features include the ability to set request parameters, and save preferences for an individual session or permanently.