What i believe to be the best CSS solution.
.auto-resizable-iframe {
max-width: 420px;
margin: 0px auto;
}
.auto-resizable-iframe > div {
position: relative;
padding-bottom: 75%;
height: 0px;
}
.auto-resizable-iframe iframe {
position: absolute;
top: 0px;
left: 0px;
width: 100%;
height: 100%;
}
<div class="auto-resizable-iframe">
<div>
<iframe frameborder="0" allowfullscreen="" src="http://www.youtube.com/embed/_OBlgSz8sSM"></iframe>
</div>
</div>