Since long before HTML5. I suspect that it's one of my privacy-protecting plugins. It's not Flash, as I have no problems with youtube videos. Often, even the preview static image doesn't show up, just a big white space. For a while, I was able to play them by going to vimeo's site and playing them in 'couch mode'. But no more.
I've hunted through the Vimeo forums. Their FAQ says something like "you must have at least Flash version, er, 3.0, or something". Flash is always the lastest, within three days.
Listen, they're usually just little funny cat-meme-like videos. I can live without 'em.