I know FireBug with YSlow has to be by far my personal favourite. I also use IE developer toolbar when forced to test pages in IE. Is there any other jewels out there hiding??
Well you already mentioned FireBug, so the next web-related tool I use a lot would be IE Tester (http://www.my-debugbar.com/wiki/IETester/HomePage).
It's a single browser that lets you use IE 5.5, 6, 7 and 8. It's not an "add-on", strictly speaking, but I think it still qualifies :)
Selenium IDE - Acceptance testing has made my life so much more stress free.
In Firefox, both Live Http Headers and User Agent Switcher are indispensable.
Although I work in a .NET shop, Firefox is my go-to browser, just based on the richness of the add-ons and stability of the core browser.
If you're on a Mac, quit Safari, and then cut and paste this into a Terminal window:
defaults write com.apple.Safari IncludeDebugMenu "YES"
For Internet Explorer, the IE Developer Toolbar, as you mentioned, is very very useful. It allows you to navigate through rendered HTML, and it will display the section on the screen (highlighted block). I consider it mission critical for debugging rendered HTML.
Also of great use is Fiddler. Fiddler is a HTTP Debugging Proxy which logs all HTTP traffic between your computer and the Internet. Fiddler allows you to inspect all HTTP Traffic, set breakpoints, and "fiddle" with incoming or outgoing data.
It's not strictly an add-on, since it's included as part of the browser, but I've been finding Dragonfly[1] to be really useful.
It has all most of the features of FireBug and works out of the box in Opera.
I used to love fiddler but hated how hard it was to work with Firefox. Also, the whole not debugging of localhost (an early problem, may be fixed in most recent builds) was a big annoyance during local development.
Then I discovered FoxyProxy and life has been sweet ever since. I also use Firebug with YSlow. The only time I use IE is for final script/css/layout tests.