When I hide a YouTube video, it stops playing. However, this is not the case for Vimeo videos. Is there another way to stop a Vimeo video?
Vimeo has a JavaScript API that allows you to access and invoke many properties and methods on the video player (including pausing the video and also unloading it completely). They also have an API Playground and some examples on GitHub.
[Edit]
Since you mention that you use the Universal Embed Code, here are some caveats from the web site:
With the Universal Embed Code, the only way to interact with the player is by using window.postMessage. postMessage is a relatively new development, so it's oly available in the following browsers: Internet Explorer 8+, Firefox 3+, Safari 4+, Chrome, and Opera 9+.
Because of the complexities involved with postMessage, we've written a JS mini-library that does all the hard work for you! You can find it on the downloads page or you can see some examples below.