Make all WP oEmbedded videos responsive.

functions.php

<?php


/**
 * Wrap an embedded video with a container for simpler styling.
 *
 * @since  1.0.0
 *
 * @param  string $output HTML Markup.
 * @param  string $url    oEmbed URL.
 * @return string         Potentially modified HTML markup.
 */
function my_theme_oembed_video_wrapper( $output, $url ) {

	// Setup list of providers to filter
	$video_providers = array(
		'youtu\.?be',
		'vimeo',
		'hulu',
		'viddler',
		'wordpress\.tv',
		'funnyordie',
		'slideshare',
		'dailymotion',
	);

	// If oembed is from a provider, wrap it
	if ( preg_match( '/' . implode( '|', $video_providers ) . '/', $url ) ) {
		$output = '<div class="video-wrapper">' . $output . '</div>';
	}

	// Return output
	return $output;

}
add_filter( 'embed_oembed_html', 'my_theme_oembed_video_wrapper', 10, 2 );

style.css

/**
 * Make sure embeds and iframes fit their containers
 * Source: http://css-tricks.com/NetMag/FluidWidthVideo/Article-FluidWidthVideo.php
 */
.video-wrapper { /* 16:9 */
  position: relative;
  padding-bottom: 56.25%;
  padding-top: 25px;
  height: 0;
}

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