The following is a list of addons that I find extremely useful when searching for security loopholes in web applications using firefox.
This addon allows us to calculate common types of hashes and provides us with some common encryption methods. It also allows us to edit post data and referrer on fly.
This addon becomes your best friend when it comes to editing POST or GET requests. This particular addon eliminates the use of intercept proxies when the job is to manually modify the request headers and post data. It also displays the time taken for a response to come from webserver, which is helpful in Blind SQLi.
This addon is another utility to play with the headers. It allows us to repeat HTTP requests by slightly modifying the parameters.
The most popular addon among web developers. It allows you to edit HTML code in your browser, provides interface for playing with cookies, js console and many more features. It is better to add Flash firebug also which gives the capability to edit AS3 files in the browser itself.
Though this addon doesn't provide any active service in vulnerability assessment, it helps a lot in a passive manner. It provides an easy interface for switching between different proxies. We can also whitelist and blacklist urls. It even has the facility to automatically switch between proxies based on the predefined url matchings.
Even though my list officially ends here, I would like to add two addons provided by Security Compass for firefox. One is SQL inject me and the other one is XSS Me. Their functionality is very clear from their names.
UPDATE - I recently came across another addon called Fireforce which helps in bruteforcing web application forms.