The bbc have published an article Websites alienate Firefox users" which describes how many websites do not work properly for firefox users. This is quite a conservative way of phrasing it - do not work at all in any non-IE browser is how I'd have said it.
One of the examples given is odeon.co.uk (who didn't have the foresight to setup odeon.co.uk to work, you need www.odeon.co.uk..). I've tried to complain to odeon before about their site, but they do not publicise a contact address (or didn't anyway). In the last few months or so they have been offering a text only version of their times and booking system which does work properly in firefox.
I'd be interested to see statistics of how often that was used in comparison to the "main" interface.
Microsoft made quite a blunder in withdrawing Internet Explorer for the apple macintosh. Now web designers are forced to consider other browsers, or risk losing the rich and trendy mac market.
I choose to take issue with two other aspects of this article. The first is referring to firefox as standards compliant. What does that mean? That it renders all HTML/CSS flawlessly? false. That it does not incorporate it's own little flares and non-standard extensions? false. The second is the quoted market-share figures, which are almost certainly somewhat inflated by the under-hyped prefetch feature.