Officially the male members of the Royal family dont have one. Mountbatten-Windsor has been proposed, but apparently its a constitutional mess. "Wales" is used as Harry's and Willie's surname as a stop-gap.
EDIT : http://en.wikipedia.org/wiki/Prince_William,_Duke_of_Cambridge
"For the male-line grandchildren of Elizabeth II, however, there is currently some uncertainty over the correct form of family surname to use, or whether there even is a surname. The Queen has stipulated all her male-line descendants who do not bear the titular dignity of prince shall use Mountbatten-Windsor as their family surname (although Letters Patent exist stipulating the name Windsor, but with the same caveat). According to their flight suits as seen in television interviews, Princes William and Harry both used Wales as their surname for military purposes; this continues to be the case for William since his creation as Duke of Cambridge"