QE2, and I believe Holland America. American Steamboat, also. You can always ask any cruise line directly if they have a singles special going on whereby you'll have a cabin to yourself and not have to pay a single supplement.
There are deals to be had on the solo occupancy. A lot of them are "last minute" deals. For calling early in the booking process, like Katie said, the Carnival 1A ones solo are just are really close to the having roomate prices. The cabins are on the lower decks and have a twin bed and a fold down bunk and are inside cabins. They go pretty fast so book early and you usually need to call your carnival "personal cruise representative". I don't know if they have them on the newer Carnival Ships. They can even be booked with a roomate for even cheaper per person rate. (you both have to pay the port charges) the bunks look ok except if you are a BIG person...........but again you have to mention them because they are not on the online announcements. I've never booked one but I did sleep in one once....(NO NOT katie's although I would like to). some people I know have booked those cabins and have gotten very nice upgrades to higher decks and I think its called a 4 A cabin. One guy even said he got an ocean view cabin upgrade...........but he could have been lying. The ship doesn't sway as much on those lower decks which apparently important to some people, but its a LONG way upstairs to the lido deck, so locate the public restrooms upstairs. lol . there is a a really good travel agent who books solo occupancies last minute and far in advance ones.........and also one or more Yahoo boards that focus on single occupancy cabins, but I don't think it is within the rules of this board to post that sort of thing.
John G. I had one of the cabins you described on a Norwegian cruise 2 years ago. I was upgraded to an outside porthole cabin.
Carnival Elation 6/02
Dawn Princess 10/02(2 cruises, back 2 back)
Regal Princess 1/03
Regal Princess 4/03
Norwegian Star 11/03
Norwegian Wind 4/04
Dawn Princess 5/04
Norwegian Wind 9/04
Carnival Spirit 11/04
Norwegian Wind 3/05
Holland America Ryndam 5/05(2, back 2 back)
Carnival Liberty 9/05
NCL America, Pride of America 12/05
Norwegian Wind 4/06
Carnival Liberty 11/06
Cunard's QE2 has the best selection of single staterooms in all categories, from the deluxe to the economy, for which there is no surcharge. Queen Mary 2 charges 175-200% surplus. I recently crossed the Atlantic on QE2 in a single and dined in the Caronia Restaurantt at a table for 2 to myself. I was pampered. It is a wonderful ship for singles who are not interested in all the wild partying one associates with mainstream cruiseships and cruise lines. I believe there are also singles on SagaRosa (formerly Sagafjord) and SagaRuby (formerly Caronia and orignally Vistafjord).