There have been a few videos around since as far back as 2010 that people can run on water. This is less commonly called Liquid Mountaineering. This is apparently a new sport but I have only ever seen videos of people doing this, e.g http://www.youtube.com/watch?v=Oe3St1GgoHQ
The Mythbusters tried this and they came to the conclusion that this myth was "busted" but as we should all know that we should not take what these guys do as a bible. The myth here: http://mythbustersresults.com/running-on-water
There seems to be alot of debate over this in comments of the running on water videos as you can hide a platform under the water which will make you look like you are running on water. This means it could be a simple illusion of running on water that actually running on water.
Definition of "Running on water": Running on water is the art of running un-supported on water, to remain on top of the water for a given series of steps on the water.