I would think you have to pay a single supplement on many of the lines.
You might want to look into Quark--You can pay a single suppplement if you want your own cabin--however they will match you up with another solo traveler of the same sex if you prefer--if they don't have another solo traveler to match you up with you get the cabin to yourself without the single supplement. (at least that was the offer a few years ago when I was looking into going solo, not sure if they still have this policy)