Have you considered something like this?
http://world.episerver.com/Blogs/Jeff-Wallace/Dates/2013/3/YouTube-Block/
That could work Torjus, except that I'd like to be able to embed responsive videos in the main content as well as a block, and seems to only support YouTube (not Vimeo and friends). In the meantime, I've updated my css to use class .embed-container instead of .video-container. That way, I can require that editors paste the output from embedresponsively.com. The TinyMCE editor / EPiServer will strip most of the code, but it will leave the div with class .embed-container. Not ideal, but as a hack it might be sufficient for our needs.
I am using the Twitter Bootstrap framework to get a responsive design for my site. What I am trying to do now, is have it work with embedded media also. I have tried using flex-video css, fitvids.js, fluidvids.js, and EmbedResponsively.com, but it always overflows its container:
Any suggestions to get responsive media working?