Eirudo

A lightweight plugin to embed YouTube videos while keeping the correct aspect ratio — all with a simple shortcode.
<ul>
<li>Very simple shortcode. Use it in posts or widgets.</li>
<li>Uses the default YouTube iframe embed, but fully responsive.</li>
<li>Custom aspect ratio if you want a different video size.</li>
<li>Automatically centered, so your video always looks neat in your content.</li>
<li>Lazy load support to improve performance.</li>
<li>100% free — no ads, no trackers, no funny business.</li>
</ul>
<h3>Arbitrary section</h3>
<h3>A brief Markdown Example</h3>
Pros: 
1. Simple and lightweight — one shortcode per video 
2. Lazy load support 
3. Extra parameters available for advanced users
Cons: 
1. Designed for simple embeds only (no playlist support, one video per shortcode)

Simple YouTube Responsive

Perfect

You can add a line to your functions.php to make videos responsive if you're doing your own theme. However, if you're not, this plugin works beautifully and gives other options like lazy load, etc. 

If doing your own theme, add: add_theme_support( 'responsive-embeds' );

Works Beautifully

Easily embed responsive YouTube videos using a simple shortcode. Lazy load included.

Thomas

Responsive Embed Videos allows you to easily add youtube or vimeo videos to your website using our shortcode like :
[rev video=’http://youtube.com/watch?v=whatever’] or [rev video=’http://vimeo.com/whatever’]
All videos embeded with this shortcode will be fully responsive.
Here is a list of the shortcode attributes :
video – default: none | This is the url of your video, from youtube or vimeo only for now.
width – default: 100% | This is the width ( in % ) of the player.
align – default: center, left, right | The horizontal alignment of the video.
ratio – default: 16/9 | This is the ratio we use to resize the player.
style – default: simple, normal | This is the style of the player.
Languages: English.
Disclaimer :
I can’t guarantee a 100% compatibility with advanced themes who may already make the embed videos responsive or with other video plugins.

Responsive Embed Videos

This plugins makes your embed videos included with its shortcode responsive. Compatible with Youtube and Vimeo.

Simple YouTube Responsive vs Responsive Embed Videos