Firefox is legitimately better than IE in almost every way. Tabbed browsing (multiple pages in one window) alone is worth the switch. It blocks popups by default, has a built-in search bar, and gets security updates way faster than IE. Plus it has extensions — little add-ons that customize the browser. AdBlock is essential. And yes, it works with all websites.

The main reason to switch is security. IE is deeply integrated into Windows, so IE vulnerabilities become Windows vulnerabilities. Firefox runs in its own sandbox. I haven't had a single spyware infection since switching. The only sites that don't work in Firefox are some corporate intranets that use ActiveX, and Windows Update. Everything else works fine.

I switched to Firefox 6 months ago and won't go back. The tab feature is amazing — I used to have 15 IE windows open and it was a nightmare. Firefox also remembers your session so if it crashes, all your tabs come back. The memory usage can get high with lots of tabs open though. Opera is also worth checking out if you want alternatives.