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.

Le-Pixel-Solitaire

The “Enhanced YouTube Shortcode” plugin provides a quick & easy way to use a custom YouTube© player in your posts and/or pages without having to get your hands dirty in the source codes! The main advantage over the way WordPress is working this out is the possibility of changing the display of all players in one single spot instead of having to do it manually at every places it has been set. But most importantly: it’s fun and good for you! (check out the screenshot for a sample of all offered options!)
Now with more than 10 parameters available through a simple configuration page (reach it from the Settings Menu), the code that is generated always allows scripting access and forces the use of the ActionScript 3 engine (see Other Notes for limitations). It has been initially created on a WordPress 3.2.1 live installation & recently tested on a WordPress 3.9.1 live installation with success, according to the specifications of the official <a href="http://code.google.com/intl/fr-CA/apis/youtube/player_parameters.html" title="YouTube Embedded Player Parameters - Google Code" rel="nofollow ugc">YouTube Embed Player API Parameters</a>.
There are a couple of things on the To Do list (see Other Notes) & the developer is back on track with this project so you can expect a major upgrade soon (summer 2014)!
<h3>Limitations</h3>
<ul>
<li>
Internet Explorer is not a natural friend of YouTube… Every versions of this browser, from 6 all the way up to 9, have different bugs & even more ways to deal with YouTube videos. So in order to push a video to everyone this plugin will provide a player to Internet Explorer effectively but without other parameters than width & height. All the rest will be the default state of a “regular” YouTube video player. A future version should solve those issues by serving an all javascript player to this browser.
</li>
<li>
The tests on WordPress 3.9.1 were quick, some features may be not working but this should not affect the plugin responsiveness. All bases will be covered in the next major release of the plugin (v3).
</li>
<li>
Some WordPress themes that already have a bunch of shortcodes may cause conflicts with this one. Usually a quick look in the doc of your theme & you’ll find a way of injecting “raw” codes in your post without triggering any presets options.
</li>
</ul>
<h3>TO DO</h3>
In the plan for the next major upgrade (v3) :
<ul>
<li>
Rewrite the core of the display functions.
</li>
<li>
A simpler/quicker way of inserting the shortcode.
</li>
<li>
HTML5 implementation.
</li>
</ul>
In the back of my mind…
<ul>
<li>
Develop some «height & width» presets.
</li>
<li>
Google Analytics integration.
</li>
<li>
Take over the world.
</li>
</ul>
Not necessarily in that order…
<h3>License</h3>
This plugin (and all its related files) falls under the <a href="http://www.gnu.org/licenses/gpl-3.0.txt" title="GNU General Public License - Version 3" rel="nofollow ugc">GNU GENERAL PUBLIC LICENSE v3</a>.

Enhanced YouTube Shortcode

A quick & simple way to include YouTube videos in your Wordpress posts with a neat centralized options panel to manage the player's output.

Simple YouTube Responsive vs Enhanced YouTube Shortcode