The embed code:

<div class="videoWrapper">
<iframe width="560" height="315" src="https://www.youtube.com/embed/7gd-EHb2nnc?showinfo=0" frameborder="0" allowfullscreen></iframe>
</div>

The CSS:

.videoWrapper {
	position: relative;
	padding-bottom: 56.25%; /* 16:9 */
	padding-top: 25px;
	height: 0;
}
.videoWrapper iframe {
	position: absolute;
	top: 0;
	left: 0;
	width: 100%;
	height: 100%;
}