The issue of Water on Mars is about as fundamental as Life on Mars. Certainly, water exists in the ices of the N.Polar Cap (and probably the S.Polar Cap). Also Water is found as a vapor and ice crystals in the the Martian atmosphere. Even Clouds of moisture are known to form. However, as with the CO2, liquid water can not exist in the low pressure environment of the Martian Surface. When water ice warms up, it immediately evaporates into the atmosphere.
What about in the past?
Apparently, yes. There is evidence from:
Craters. Among the oldest craters (> 3.5 b.y.o), large craters
show significant erosion. Smaller craters appear to be entirely destroyed.
This may have been caused by flowing water.
Flows and Islands Tear-drop formations, which could only
be explained by flowing water.
Dendritic Valleys Looking similar to water carved steams.
Mars Rover Opportunity Found stong evidence that parts of Mars
was soaking wet in the past. See here
This all suggests a warmer climate with liquid water. But how? It's not just the cool temperature which is the problem. It's the low atmospheric pressure!
Theory
Early in Earth's history, there was a LOT of CO2 in
the atmosphere from volcanism. Also, numerous impacts kept the
surface much hotter, evaporating a lot of the water/CO2
in the ground. This increases the greenhouse warming. Also, all this
stuff in the atmosphere, will increase the pressure on the ground!
This likely was happening on Mars early on, too. This might ALSO
have been when Mars lost most of its atmosphere!