http://webdesignerwall.com/tutorials/css-elastic-videos

.video-container {
	position: relative;
	padding-bottom: 56.25%;
	padding-top: 30px;
	height: 0;
	overflow: hidden;
}

.video-container iframe,  
.video-container object,  
.video-container embed {
	position: absolute;
	top: 0;
	left: 0;
	width: 100%;
	height: 100%;
}

<div class="video-container">
	<iframe src="http://player.vimeo.com/video/6284199?title=0&byline=0&portrait=0" width="800" height="450" frameborder="0"></iframe>
</div>

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How to Create Fixed Width & Elastic

.video-wrapper {
	width: 600px;
	max-width: 100%;
}
HTML
<div class="video-wrapper">
	<div class="video-container">
		<iframe src="http://player.vimeo.com/video/6284199?title=0&byline=0&portrait=0" width="800" height="450" frameborder="0"></iframe>
	</div>
	<!-- /video -->
</div>
<!-- /video-wrapper -->