Every month I get a question from clients regarding the ability to embed video in email HTML templates. Unfortunately, the answer is that you cannot when using most email clients.
For the vast majority of desktop, tablet and mobile email clients, the answer is no, even with HTML 5.
I found this chart from Email on Acid (they also supply all of the HTML code) that does a good job laying out the state of video support in email. From a market share perspective, about half of emails sent can support playback within the email client and a half cannot. Developers should code html so that the default image displays in any client that does not support video, particularly since some clients will display the video player, but the video is unplayable, creating confusion.
Net, the idea to embed video in email is still a bad idea unless targeting Apple Mail and Samsung Galaxy customers specifically that use the native mail applications of those platforms.