mch0lic

Simple Video Gallery (SVG) is easy to use plugin that allows adding videos and playlists (series of videos) into your blog page or post. Currently SVG supports only youtube.com videos with other services to be supported upon request. Plugin has built in stylesheet editor and therefore it should be quite simple to adapt the looks you desire.
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Translations Credits 
Serbo/Croatian – Borisa Djuraskovic

Simple Video Gallery

Simple video gallery plugin for WordPress!

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.

Simple Video Gallery vs Simple YouTube Responsive