Eirudo

Embed YouTube videos and keept their aspect ratio, just using simple shortcode.
<ul>
<li>Simple shortcode, can be used in the posts or widgets.</li>
<li>Using default YouTube Embed Code (iframe), but make it responsive</li>
<li>Custom aspect ratio, if you want set different porpotion size.</li>
<li>Auto centered position. So if you insert it on your post section, the video always on center-aligned.</li>
<li>Lazy Load supported.</li>
<li>100% Free! And no ads or even trackers inside.</li>
</ul>
<h3>Arbitrary section</h3>
<h3>A brief Markdown Example</h3>
Pros: 
1. Simple, only using shortcode to use for individual video each shortcode 
2. Lazy Load supported 
3. Custom parameters for advanced use
Cons: 
1. Only for simple use,not for advanced playlist. Embedding one video for each 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

Embed responsive YouTube videos using simple shortcode. Lazy Load supported.

Kodetop

WP Youtube Player allow insert Youtube videos on WordPress using a single quicktag <code>[tube][/tube]</code>
Features
<ul>
<li>Easy install</li>
<li>Embed Youtube movies with simple code</li>
<li>Panel for easy configuration</li>
<li>Config Player version (AS2 & AS3)</li>
<li>Support config themes for player</li>
<li>Support HTML5 Player</li>
<li>Support tubePlayer (http://blog.unijimpe.net/tubeplayer/) for play videos.</li>
<li>Generate <code><object></code> code for Feed compatibility </li>
<li>Generate <code><object></code> code optimized for iPhone</li>
</ul>
For insert single youtube video on Post Content or Text Widget you can use ‘Youtube URL’, ‘Youtube Embed URL’ or ‘Youtube Video ID’:
<pre><code>[tube]http://www.youtube.com/watch?v=AFVlJAi3Cso[/tube]

[tube]http://www.youtube.com/v/AFVlJAi3Cso[/tube]

[tube]AFVlJAi3Cso[/tube]
</code></pre>
To insert video with specific size can user width and height:
<pre><code>[tube]http://www.youtube.com/watch?v=AFVlJAi3Cso, 500, 290[/tube]
</code></pre>
To insert video on template, use the php code:
<pre><code><?php wp_youtubeplayer("movie.swf", "width", "heigth"); ?>
</code></pre>
For more information visit <a href="http://blog.unijimpe.net/wp-youtube-player/" title="plugin website" rel="nofollow ugc">plugin website</a>

Simple YouTube Responsive vs WP YouTube Player