Firefox is an excellent tool for SEO. I can't imagine working without it. Here are the top 10 Firefox SEO extensions that I use every day:
The Web Developer Toolbar has many indispensable features for both Web development and SEO. It allows you to easily manage cache, cookies, referrers, JavaScript, CSS, and much more. For example, you can disable CSS on a page with Ctrl-Shift-s. You can quickly disable cookies to see how a site changes with cookies off. You can show alt attribute text on the page. And much more... The Firefox Web Developer Toolbar is an essential tool.
The User Agent Switcher Firefox extension allows you to visit Web sites as Googlebot. This is a great way to check for search engine cloaking
The Search Status Firefox extension shows you Google PageRank in the status bar. It also allows you to view rel=nofollow links on pages, like on the Wikipedia page shown in the image below.

The following image shows the PageRank displayed in the status bar, as well as the many menu options available.

The HTML Validator extension shows you HTML errors when you view the source of a page, allowing you to quickly spot areas in the source that might present difficulties to search engines.
The following image shows the HTML validation errors on the Google home page. The highlighted lines indicate HTML errors or warnings. The bottom left box lists all of the problems, and the bottom right box offers documentation related to the HTML error.

The Show IP Firefox extension displays the IP address of Web sites in your Firefox status bar as shown in the image below. This is useful for checking to see if Web sites are being hosted on the same IP or same C-block.

The Live HTTP Headers extension lets you see the HTTP headers scroll by as pages load. Just use Alt-l to open and close the extension in the sidebar. This extension is essential.
The X-Ray extension displays HTML tags superimposed on top of Web pages while you are viewing them. It's an easy way to check for HTML headers and other elements as shown in the image below.

The NoScript Firefox extension turns off JavaScript for all sites by default and lets your override that setting on a site-by-site basis. Since search engines generally don't surf with JavaScript, you can get a better idea of how sites look to search engines if you have JavaScript off. This extension is highly recommended. The image below shows JavaScript being blocked on a spam page that is probably about to use JavaScript to redirect.

The Customize Google extension puts links to other search engines on the Google SERPs so that you can quickly search Yahoo and MSN right from the Google SERPs. Screenshot below:

To take a screenshot of Web pages (e.g., for client reports), use the Screengrab extension. It allows you to capture an entire Web page even if it goes below the fold:

If you are on GNU/Linux, there are many ways to take a screenshot.
Firefox profiles are a great way to manage different extension profiles on one computer. You can set up Firefox so that you have one profile with one set of extensions (e.g., with NoScript and User Agent Switcher so that you can browse as Googlebot), and another profile for general browsing.
For more Firefox extensions, check out the article Best Firefox Extensions Revisited. For more about SEO, check out the Intro to Search Engine Optimization resource.
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Comments
Thanks!
I love these extensions. Been using some of them for ages, but they all look great. Cheers.