1. IE-based — and there are so many variations between, say, IE 5 for Windows, IE 5 for Mac, and IE 6 for Windows that they may as well be different browsers as far as testing is concerned.
2. Gecko-based — that’s Firefox, Mozilla, Camino, modern Netscape, etc. For the most part, these will all work the same.
3. KHTML-based — Safari, OmniWeb and Konqueror. There were some major fixes between the Jaguar and Panther versions of Safari, and IIRC OmniWeb is still based on the older one, but these can be taken as a group as well.
4. Opera

(And yes, I’m ignoring the ancient Netscape 4 and IE 4.)

I’ve found that generally, if you use standards-based techniques (A List Apart is a great source for these) and do your main testing in a Mozilla-based browser, 95%+ will either work perfectly or display OK in Safari, Opera, etc., and 80-90% of it will work in IE. It’s sometimes a pain to get IE to handle it right, but if you start with good code, it’s usually a matter of finding the right tweak for IE rather than starting with IE-based code and ripping things out to get it to work in other browsers.

Also, Firefox itself has some excellent extensions for web developers, including a validation add-on for view source, a color picker that lets you match colors in a web page, and a toolbar that lets you selectively enable/disable features, outline specific types of elements, and so on.