You mean .hasClass('class')...? Or simply .is('.class')? (A bit slower though.) If you want to assign a class, use .addClass('class') or .toggleClass('class'). The opposite is .removeClass('class'). If you want to get a list of all classes, you'll have to rely on $()[0].className or $().attr('class'), AFAIK.
Well, there's nothing wrong is using className (or anything purely JS) even when jQuery equivalents are available. I usually choose to use jQ in these situations because the code is shorter and thus compresses better.
Speaking of which, I just finished rewriting Zoomedia... The code works much better, and is about 150 bytes shorter :D