I used NCSA Mosaic when it first came out. Then Netscape. Since I used a Sun workstation to browse the 'net at the time, Internet Explorer wasn't an option until IE 5.5 I believe. Microsoft created a Windows layer that could be installed on a Sun box which then let you install IE. The extra layer really added some bloat to the system and it never really worked well. I also tried Opera on the Sun box which also didn't work very well (the graphics and layout was always pretty mucked up).
With the security issues that popped up surrounding IE 6, I pretty much stayed with Mozilla or Opera on my Windows systems. I also have a few Linux systems kicking around including on my work Ubuntu workstation (laptop is WinXP Pro). Since I'm comfortable with Firefox, I pretty much stuck with it and avoid IE.
I use Firefox on my Mac as well even though it does make the laptop run a bit hotter. Mainly because of AdblockerPro and Flashblock. I don't have many other plugins installed on the Firefox installations.
Mainly though, from looking at my list, Firefox works on all of the platforms I use. Windows, Mac, Ubuntu, and Solaris. IE doesn't and it's a pain to do things one way on one box and differently on another.