Alex Raven

This plugin adds a button to post editor to insert videos and video playlists easily. Simply click the button, paste YoutubeURL 
and kick Insert Video. Support for other video hostings will be added later. Video embedding can be used as a shortcode in posts 
and pages, including custom post types.
A few notes about the sections above:
<ul>
<li>Simple button in editor to add videos to your pages and posts</li>
<li>Video is embedded responsively – will fit the container, keeping aspect ratio</li>
<li>Supports the following parameters: controls (on/off), autoplay (on/off), autohide controls (on/off), loop (on/off)</li>
</ul>
By clicking > Insert Video button it opens a popup window where you can paste video URL and set parameters. You can also set start time, 
or just leave it 0:00 if you want to play video from the beginning. Playlists are also supported.
It also stores a list of recent videos where you can chose one of the videos you have used before (or saved for future). In later versions, 
there will be something like a video library to access and share videos between multiple wordpress administrators and editors.
This plugin was a part of another bigger project. It was handy and easy to use, so I decided to extract the code to a stand-alone 
plugin and make it available for free for public.
<h3>Usage</h3>
When you use > Insert Video button in post / page editor, it adds a shortcode automatically. Alternatively, you can put a shortcode manually:
[rem_video id=”XXXXX” list=”YYYYY” autplay=0 controls=1 autohide=0 loop=0]
XXXXX is a video ID from Youtube URL, it comes after <code>v=</code>, like https://www.youtube.com/watch?v=mbBmc8RC_S8 
YYYYY is a playlist ID (for playlists), like https://www.youtube.com/watch?v=mbBmc8RC_S8&list=PLCF042F294768BFD1 
autoplay=(0|1): if 1, video will start automatically when your page is loaded. Default is 0 – video will not start automatically. 
autohide=(0|1): if 1, it will hide controls when video is played. Default is 0 – controls will be always visible. 
controls=(0|1): if 1, controls will be shown, if 0 – hidden. Default is 1. 
 loop=(0|1): if 1, when video is ended, it will start from the beginning. If it is a playlist, it will loop from first video in the list.

Responsive Video Embedder

A simple but powerful plugin to embed videos responsively into your Wordpress site. Works with both videos and playlists.

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.

Responsive Video Embedder vs Simple YouTube Responsive