Well, that is what the LCROSS mission is trying to find out!
LCROSS stands for Lunar CRater Observation and Sensing Satellite
On October 9th 2009 NASA was hoping to find out by crashing a rocket into the moon. By doing this, they are aiming to create an impact crater that forces water and ice vapour above the lunar surface for analysis.
For more information, have a look at the NASA LCROSS site at: http://www.nasa.gov/mission_pages/LCROSS/overview/index.html
NASA also set up a site for amateur observers at: http://lcross.arc.nasa.gov/index.htm
At the amatuer site you can watch a movie about the mission and even the Download the song “Water on the Moon” written by LCROSS Deputy Project Manager John Marmie! Performed by John Marmie and Jeff Petro.
Check it out!