I recently embedded a few Daily Show clips hoping the auto-play problem was gone. I had tested on Chrome (Safari doesn't have the problem) and thought it was fixed but when I tried again today I found multiple clips auto-playing. (It's really bad if you go to the dailyshow tag on this blog).
For me the problem was using the extension AdBlock Plus on Chrome. I turned this off and it didn't auto-play, turn it on and it did. It turns out Chrome has a better option, set all plugins to require Click to play. This post from DailyKos, where they had similar problems, explains how to configure that and also has some options for Firefox that I did not try. Embedded videos playing automatically at DKos? Let's look at that.
Let me know if that works for you or if you continue to have issues. I'll probably start embedding clips again in a few weeks.