Webamator

YouTube iframe embeds often load many unnecessary resources, which slows down your page. YEP: Optimize YouTube Embeds is a lightweight WordPress plugin that replaces YouTube iframes with a clickable preview image. 
The actual video loads only when the user clicks the play button, improving page load times and reducing initial page size.
<h3>External services</h3>
This plugin uses the external YouTube thumbnail service (https://i.ytimg.com) to display preview images of YouTube videos. 
When a page with a YouTube embed is loaded, the plugin requests the thumbnail image directly from YouTube servers. 
No personal data is sent from your site to YouTube, only the video ID (already public in the YouTube URL).
Privacy Policy: https://policies.google.com/privacy 
Terms of Service: https://www.youtube.com/t/terms

YEP: Optimize YouTube Embeds

Short Description: Load YouTube videos faster by replacing iframes with a preview image; the video plays only when clicked play.

Square One Media

Richard Webster

It’s never been easier to include responsive Youtube and Vimeo videos on your website. From a simple, intuitive interface you can insert a video right into your posts, pages, and widget areas within seconds. Include a description of the video, customise the look and feel, comes with multiple sizes to choose from that are fully customisable, and several video alignments are available.
A shortcode is generated and is used to create the content. Included in the plugin are shortcode generators so you can create one without worrying about how to write a shortcode manually.
Full supporting information is built right into the plugin with a bespoke plugin settings page. Shortcode information fully documented.
Get started today!

Responsive Videos

Finally one that works, after trying about 5 of the popular ones, this was the only one that actually made my video responsive using the Mayatheme and also allowed to play friendly within other column shortcodes. Thanks very much and keep up the good work :)

Finally one that works!

An easy way to add mobile responsive videos to your posts, pages, widgets, and other content areas.

YEP: Optimize YouTube Embeds vs Responsive Videos