The current theory explaining Mars' reddish color-- which is obvious enough to the naked eye that the ancient Greeks and Romans named the planet after their gods of war-- holds that liquid water running over the surface essentially rusted the rocks.
A new theory, however, suggests that hermatite, the red component of the Martian surface, could have been created by erosional processes. In that case, running water on the surface is not necessary.
The new theory is interesting, but there's a good case to be made that water did in fact exist on the surface at some point in the past. We know water ice exists just under the surface today. Channels on the surface seem to have been cut by flowing water. There are also geologic formations that seem to be ancient lakebeds, and theories arguing that Mars once had a thicker atmosphere that could have supported surface water. Perhaps the truth will turn out to be that both erosion and flowing water played parts in turning Mars red.