I have such things in the DNA Lounge weekly mailing, and some time recently (possibly with MacOS 10.8 or possibly earlier) the videos are showing up as an unclickable black box when viewed in Apple's Mail.app. If I embed them using the old-style embed way instead of the newfangled iframe way, then I get a gray box that says "Blocked Plug-in".
They don't seem to work on the iPhone mail reader either. The iframe way is unclickable, and the embed way shows the thumbnail but then when you click it, the Youtube player says "the operation could not be completed."
The question I am trying to answer is: is the number of people who are able to click play on a video embed in an HTML email message small enough that I should just stop embedding them at all?
I sure do love playing whack-a-mole to figure out what random parts of my messages the various "sanitizers" throw away. My favorite part is that you can't reliably use "margin" in your CSS. That's just great.
In my experience, literally anything but a, b, font, i, or img is a crapshoot, and better served by a thumbnail linked to the real thing.
Your mileage may vary.
I've never seen an embedded video work in any mail reader, ever.
However, gmail probably comes closest in that it will provide a thumbnail link to a YouTube videlo based on the context.
I'd skip the HTML and just put in a link.
My experience is similar to Jake's i.e. I usually take a screenshot/thumbnail and link it to the real thing, speaking of youtube videos, the end results is something like this: http://cl.ly/image/3q0J1q2a2l3P