Only a little, as it turns out. Simon writes with this comparison of 100 corporate sites in IE 6 and the newly-released IE 7. Thirteen of the sites have what seem to be small issues as a result of the browser upgrade:
It’s worth pointing out however that the general lack of adherence to web standards amongst the FTSE 100 companies may have insulated them somewhat from IE7’s various bugs and glitches (IE7 tends to struggle most with standards-compliant sites – particularly those using hacks and filters to achieve decent presentation in IE6). Given that most sites aren’t standards-compliant however, we think our results are pretty representative.
100 websites isn’t really a large enough sample, but I’m actually impressed by the lack of serious breakage on the part of IE 7. Anybody want to try the same thing with Firefox?
DarrenBarefoot.com 
In my experience, most site breakage is due to the designer of the website, and most of it is due to non-standard issues with IE, not Firefox.
BCIT sent out an email with the following:
If you install IE7 on your home computer, be advised that some BCIT standard applications may fail to work.
Umm, I have to disagree about IE7 handling standards-compliant sites. It hardly struggles. It’s not as good as Opera, but it’s just as good as Firefox.