Primarily for the benefit of BrattyLord and Habboi, I have compiled this list of what I find are generally considered the most serious faults of IE6 and below; these are technical faults alone, not ideological ones (nothing like "abusing market advantage", etc.).
1. It cannot render webpages properly.
Internet Explorer fails to draw webpages according to what are now seven year old CSS specifications. It cannot render alpha-channel PNG images. That standard is seven years old too. If you think that failing to draw webpages isn't a complete failure on the part of a web browser, go away. Computing circles don't wait seven years for updates.
2. It is poorly-secured.
This is more debatable than the above, but people generally find that IE is less secure. Don't bother saying "I don't go on dodgy websites", because eventually, you'll always end up somewhere nasty, even completely unintentionally.
A lot of people seem to think it's no big deal to find scores of trojans on their PC every month. I am certainly not one of them, and I really don't understand the thinking behind this. IE was, years ago, tightly integrated into Windows for legal reasons, at the cost of security.
3. Slow.
On Windows, Internet Explorer is much slower than Opera at drawing most kinds of pages (source). This is a browser with the advantage of being build into the OS, too. Very poor. Firefox and Opera both support HTTP pipelining, which decreases the time taken to actually retrieve whatever is to be rendered from the remote server.
4. Lack of features.
This is, obviously, far less serious than the others. You wouldn't see me here around anywhere near as much if I had to use IE, though. I read every single new post every time I log in. I open twenty or thirty thread pages at once. If I were doing this in IE, I'd have to shift-click each topic link, then tab back to the parent window, and repeat ad luneum. I'd then have scores of pages of varying sizes and positions all over my desktop, and wouldn't be able to find my other applications.
In Opera, Firefox, etc., there are tabs (true child windows in Opera), saving my taskbar organisation. I can zim through, middle-clicking on all the topics marked as new, then right-click and roll up to the next window and get a load more up. I really ought to record a video of a visit to TWHL sometime to show you how massively more efficent it is.
All it takes is a little effort and exploration. What have you got to lose? If I didn't have my trusty Opera, well, I'd have more of a life, I suppose :). I couldn't bear the Web.
Windows users
Opera
Firefox
Other OSs
You're using something better anyway.