This website that I\'m working on has annoying alt tags popping up when you hover over links in the sidebar. I didn\'t put these alt tags in. But, I can control the CSS... I
Simple answer: no
They are impossible to turn off just with CSS. They are browser dependant and are not part of any CSS spec i.e. you can't style them, hide them, anything.
Though you can get rid of them by Javascript:
var elements = document.getElementsByTagName('a');
for (var i = 0, len = elements.length; i < len; i++)
{
elements[i].removeAttribute('title');
}