$("#id-name").css({opacity:'0.5'}).hover(function(){$(this).animate({opacity:'1'}, {queue:false, duration:350})}, function(){$(this).animate({opacity:'0.5'}, {queue:false, duration:350})});

<style>
#id-name {opacity: 0.5; -moz-transition:opacity 1s ease;-o-transition:opacity 1s ease; -webkit-transition:opacity 1s ease; }
#id-name:hover {opacity: 1.0;}
</style>

<div id="id-name">Меняем прозрачность</div>

<div id="div" style="opacity:.5;">Div</div>
<script type="text/javascript">
$("#div").hover(function(){
$(this).stop().animate({opacity:1},400);
},function(){
$(this).stop().animate({opacity:0.5},400);
});
</script>