Does Mercury have water?
Short answer: Yes, Mercury has some frozen water (ice).
Long answer: Mercury is the closest planet to the Sun so you might expect it to be far too hot to have any water. However Mercury also has some very cold areas that are able to support frozen water (ice).
The best place to find water ice on Mercury is at the north and south poles. Mercury doesn't tilt like Earth does so it's poles don't ever really face the Sun. Craters with large walls can stay completely dark, never seeing any Sun at all. This means that ice in these craters never melts.
Although we don't know exactly how much ice is on Mercury, NASA estimates that it's at least 100 billion tons1.
What about liquid water?
Mercury cannot have liquid water on the surface because it doesn't have any atmosphere so liquid water would immediately freeze (if in shadow) or evaporate (if in sunlight). However, it's possible that Mercury could have liquid water buried deep underground.
Above: Kandinsky Crater, near Mercury's north pole, never gets sunlight at its base. This is a prime candidate for finding water ice.
Image credit: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington, October 2014.
See also:
Footnotes
[1] http://blogs.ei.columbia.edu/2012/11/29/frozen-water-on-mercury-nasa-confirms/