I think it would be better to use .mouseenter().
In that case you just get 1 event, while with mouseover you get many. So your code could be:
$(document).ready(function() {
$("#icon").mouseenter(function() {
$(this).fadeOut(1000);
}).mouseout(function() {
$(this).fadeIn(1000);
});
});
You could also do this just with CSS:
#icon {
transition: opacity 1s;
}
#icon:hover {
opacity:0;
}
<img src="http://cdn.sstatic.net/stackoverflow/img/apple-touch-icon@2.png?v=fde65a5a78c6" id="icon" alt="" />