Yes, you can. The speeds are built on the Bikila platform. In the US they are advertised as a casual shoe, in Europe they are advertised as a running shoe. There is nothing wrong with running in them.
US Site:
http://www.vibramfivefingers.com/products/Five-Fingers-Speed-Mens.htm"casual wearer, after sport, travel"
European Site:
http://www.vibramfivefingers.it/product_details.aspx?model=SPEED"walking, distributes forefoot impact, running, casual"
There is no reason you couldn't run in them. They are comfortable, they breathe, and they are light.