This is a great plugin. It requires no setup after installation, works with a good selection of video sites, and fills the player screen with video very nicely at any screen size.
The only thing it could do better is detect the size of the video container and fill the container at large screen sizes.
As the previous poster mentioned, FitVids for WordPress does this, but the setup is more complicated and the author still has done nothing to make it easier (for 90% of installs, using "body" as the jQuery Selector is all that is needed). What is impressive about this plugin is that, once setup, it works for virtually all videos that you can embed on a page.
If you only use YouTube or Vimeo, then the Fluid Video Embeds plugin is your best choice. It requires no setup after installation, and does a superior job of filling the player with video at all screen sizes (as well as filling the video container).
Unlike the previous poster's comment, my experience is that Responsive Video Embeds still works fine.
Thank you, Kevin, for developing this fine plugin.