A: 

The doctype:

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"&gt;

along with the CSS :hover state provide the best results in IE8. (see this page)

Remember, IE9 is right around the corner, and may resolve many of these quirks.

Evan Mulawski
The javascript-based test cases linked above have the same performance characteristics in IE9 beta - quirks mode is fast, standards mode sucks. And this is IE9 standards mode, not emulating an older version.
Joel Mueller
New web pages have no need, and should not use, the transitional doctype. What are you transitioning from? Always use strict.
Rob
A: 

While changing the doctype may display the issue, the issue is not caused by the doctype. I can only suspect it's caused by javascript but you have some validation issues you need to address first. Validate your HTML for that list of errors.

Rob
I changed the strict example now to html5, and it validates correctly now. Makes no difference whatsoever... If I change the rendering mode to IE7 (in Internet Explorer 8) the hovering is lightning fast.
Dylan
Quit messing with the doctype! It's the very first thing that goes on a page and NEVER changes. It should have NO affect on how the browser handles this but we're talking about IE here and you can never trust IE to do anything right.
Rob
Changed it to xhtml strict, removed the javascript and changed the hovering to css :hover . Still very slow in IE8.
Dylan