WordPress allows you to embed videos so easily using oEmbed. You can easily add videos to your post just pasting their URL to your post. WordPress handles all the object and embed HTML for you. But this code is missing wmode parameter which is necessary for CSS z-index to work.

Here I will show you how to filter the HTML for the embedded video and add this parameter so easily. For this we will use the oembed_dataparse filter which is run when a user adds a video to the post. Put the following code to your functions.php file:

function stf_embed_filter( $html, $data, $url ){
	$html = preg_replace('!(<object[^>]*>)(.*?)</object>!is', "$1$2<param name="wmode" value="opaque"></object>", $html);
	$html = preg_replace('!(<embed[^>](.*?)>)(.*?)</embed>!is', "<embed $2 wmode="opaque">$3</embed>", $html);
	return $html;
add_filter('oembed_dataparse', 'stf_embed_filter', 90, 3 );

This function filters the output html and automagically adds wmode parameter to the video HTML code. And your videos will then obey the z-index values in your CSS code. If this code is missing your videos will allways show on top of other elements on your page.