nakunakifi

Embed a responsive YouTube Channel, Playlists or Videos as a Grid, List or Carousel. Display videos based on keyword.
Install the plugin and then checkout the Pro version (http://wordpress-plugin-youtube.cheshirewebsolutions.com/)
<ul>
<li>Use Shortcode to display Channel. </li>
<li>Use Shortcode to display Playlists.</li>
<li>Use Shortcode to display Videos.</li>
<li>YouTube Channel Header + Subscribe button</li>
<li>Social Icons</li>
<li>Display Videos Thumbnails in Grid, List or carousel</li>
</ul>
If you have suggestions for a new add-on, feel free to email me at info@cheshirewebsolutions.com. 
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https://twitter.com/CheshireWebSol
<h3>Credits</h3>
<ul>
<li>Google PHP Client Library (https://developers.google.com/api-client-library/php/)</li>
<li>Slick Carousel (http://kenwheeler.github.io/slick/)</li>
</ul>

WP YouTube Embed

Display YouTube Channels, Playlists and Videos as a Grid, List or Carousel!

UjW0L

This plugin lets you to display Youtube widget on sidebar with the themes that supports sidebar and Footer
It displays video and playlist of your choice with video id and playlist id. 
It also lets you display all videos from you youtube channel with option to navigate to next nd previous button. 
No google API key needed. Uses Youtube rss feed.
You have choice between single video , playlist and channel.
Note:

Simple Youtube Widget

Plugin that provides users option to display Youtube Widget on the Sidebar or Footer

WP YouTube Embed vs Simple Youtube Widget