Firefox: essential Add-ons
These are some of the addons I use to tweak my Mozilla Firefox and consider essential for most programmers, they are the reason I'm still using Firefox and not the faster Google Chrome (apart from the security problems for now).
Gmail Manager
As the title states, Gmail Manager allows you to manage Gmail accounts, it will display new e-mail notifications, amount of unread messages, amount of new messages per label etc...
Perhaps one of the most popular Add-ons for Firefox, Greasemonkey allows you to run custom Javascripts on websites to improve them to your needs. There is already a huge database with scripts available at userscripts.org.
This is a very useful tool for programmers, it can capture HTTP requests in real time, or modify and resend the request. It's extremely useful when you try to automate something, like a POST request on a website.
Still in the programming niche, Firebug shows you perfectly where the errors on your page are. It can validate Javascript, CSS, XML, ... also a nice tool to test your applications for strange input as it allows you to manipulate any element on the page - in real time.
I've discovered this Add-on only a week or so ago, but I'm already in love with it. It gives your location bar a Google Chrome feel, and has a lot of other options too, such as "Always show the Go button". I really missed that in Firefox 3 as I used that button a lot to open multiple instances of one website.
This tool will show a ticker with the latest messages on your RSS feeds, it's highly customizable and uses your "Live bookmarks" from Firefox (you know, those things you haven't ever used).
Screengrab is a handy tool to take screenshots of a website, both full page or just the current view, or a selection of a page. Useful when you need to show something on a website.
Ah... got to love this tool. It allows you to switch and store your user-agents on the fly. I mainly use this tool to spoof a Googlebot header, which allows read access on a lot of forums that would otherwise require registration, or to get past a website that only allows a specific webbrowser.
That's what I love most at the moment, maybe I'll add some more stuff to this list later.

I like the User-agent switcher trick. Maybe you should post a tutorial about that :-)