sam2kb

This plugin allows any user to add previews of websites right in the content of their posts using a simple [thumb]http://domain.com[/thumb] format. Users may also “optionally” turn on mouseover previews. No purchase or registration is required to use the plugin. Optional upgrade enables PRO features such as “Full-length Captures”, “Free Width Captures” and “Refresh on Demand”.
<ol>
<li>Easily embed website previews in posts</li>
<li>Flexible caching system allows you to store retrieved screenshots on your server</li>
<li>[opt] Display custom images for queued or error thumbshots</li>
<li>[opt] Display thumbshot URLs in a safe manner without linking them directly to the target website</li>
<li>[opt] Display mouseover header preview over thumbshots</li>
<li>[opt] Display mouseover pop-up preview over external links in your posts</li>
<li>[opt] Utilize several Thumbshots.RU PRO features</li>
</ol>
Take a look at Thumbshots.RU for more information (http://www.thumbshots.ru/en/ “Website screenshots provider”).

Thumbshots plugin

This plugin uses the Thumbshots.RU API to replace special tags in posts with website screenshots. Note: This plugin is no longer maintained.

webshrinker

This plugin will allow you to automatically show previews of external websites when a user hovers over a link in your posts. 
It’s designed to work “out-of-the-box” and no changes should be needed on your part to make it work. 
However, if you are familiar with CSS, you can apply “link previews” to links in other places in WordPress site by specifying any CSS selector that you want.
A free or paid <a href="https://www.webshrinker.com" rel="nofollow ugc">Web Shrinker</a> account is required as you will need a service API key.
<iframe class="youtube-player" width="640" height="360" src="https://www.youtube.com/embed/1xGf00XQSH8?version=3&rel=1&showsearch=0&showinfo=1&iv_load_policy=1&fs=1&hl=en-US&autohide=2&wmode=transparent" allowfullscreen="true" style="border:0;" sandbox="allow-scripts allow-same-origin allow-popups allow-presentation"></iframe>

Web Shrinker – Website Link Preview Thumbnails

Enhance your post links by enabling a popup preview thumbnail image of the destination website

Thumbshots plugin vs Web Shrinker – Website Link Preview Thumbnails