Running straight water (as in Distilled water aka pure water) won't do any harm to your cooling system as long as you do not have freezing weather (below 32*C). It will destroy anything its inside (Heads, Radiator, block, etc) when it freezes.
Never mix in or use straight tap water, it has minerals in it that will build up inside of your cooling system.

Any reason why you want to use straight water?