if ($('#element').is(':empty')){
//do something
}
for more info see http://api.jquery.com/is/ and http://api.jquery.com/empty-selector/
EDIT:
As some have pointed, the browser interpretation of an empty element can vary. If you would like to ignore invisible elements such as spaces and line breaks and make the implementation more consistent you can create a function (or just use the code inside of it).
function isEmpty( el ){
return !$.trim(el.html())
}
if (isEmpty($('#element'))) {
// do something
}
You can also make it into a jQuery plugin, but you get the idea.