There's a time and place for everything.
These videos are most useful when the web site is describing a service business, and the client/visitor would be deciding to hire that particular person. In other words, the person is the "product". I've gotten many, many compliments on my video because it's serious, to the point, and explains what I do an an 'interim vp marketing'. It not only helps establish credibility; it's actually the start of my relationship with a new client.
It's at www.Market-Savvy.com/
The other great use of video on a web site is to show an application in action: check out ShotSpotter.com
which shows ShotSpotter in San Francisco and how the service reduces gun crime in that city. How it works is very clearn there. City leaders are featured talking about their progress reducing gun violence, so it's great credibility.