Healthcare and government (US). So, so very many systems are on IE6. So, so very many websites only work correctly/fully when end users are on that platform. Until you've had to support code distributed by the US federal gov't and watch the percentages of users hitting your site from XP (or earlier) UAs rise to the double digits, you have not known sadness.

Enterprise. A lot of Enterprise applications are required for work, and require very old, very stubborn browsers.

Most emulations don't work.

You need the old stuff (IE), for the old applications to work, and as long as they can force it to, they won't update said old application.

I've even had to touch systems which required IE 4 in the last few years, from before Trident became the rendering engine.