Do cruise ships have single rooms?

Very few cruise ships have single rooms. Costa ships have them, however.

Single travelers are welcomed by all cruise companies! On ships without single occupancy rooms, single people occupying a double occupancy room are charged a "single supplement", which varies from 30% to 100% additional cost but which is occasionally waived.

At this time, there are no single rooms on cruise ships. But, yes, many people cruise solo. I have done it many times. There is a single supplement, since the ship loses money by one person occupying a room that could sleep two. However, you can often get good deals. And it's worth it to have your own room, with all its closet and drawer space. When I'm by myself, I take an interior room, one with no window.

NCL's newest ship the Epic will have special single rooms that will be available without a supplement. On other cruises a single room will cost nearly double of the advertised price for each type of stateroom.

Alot of cruises are now getting single cabins, i found a great article about the new Norwegian Epic's single cabins at http://www.sailawaywithsian.blogspot.com/

Sure do but it cost more.