Q:

Can the Flash run or walk on water? 

Can the Flash run or walk on water? 
The reason I ask is because no matter how fast he can move, he needs something to push against. 
I am assuming that he can, as hitting water at great speeds gives it the property of concrete, so to speak.  But I want to know whether he has done it or not? 

A:

I'm not sure if he's ever been depicted as doing so in the current series. [ EDIT: Yes he has, thanks to Gallifreyan] However, he was shown doing so in Ep1 of the 1990 series. 
Regardless of whether he has been shown as doing so or not, it is extremely likely that he can based on real world physics and examples.  The Basicliscus Lizard can run on water

...at a velocity of 1.5 meters (4.9 feet) per second for approximately
  4.5 meters (15 feet)...

It is calculated here that to run on water you would have to run at approximately 30m/s, or around three times faster than Usain Bolt.  Is the Flash more than three times faster than the Lightning Bolt?  The Flash has been depicted as running at at least Mach 1 which is 343 m/s.
So yes, the Flash could run on water. 

A:

Yes, the Flash can run on water, much like the common basilisk.  
I can't speak for the comics, but in the TV series it first happened in S1E5:

A:

Yes, on Superman Vol.  1 199 The Flash races around the globe against Superman, as you can see he is able to run over water

