Yes you can, but they charge quite a bit extra. Some cruise lines are better and more suited to the single traveller and offer low or no single supplements on some cruised. I cruised the Norwegian Fjords in May and the supplement was only an extra Ł100. Watch out for offers on teletext. Fred Olsen often have good deals for single travellers and so does Orient Lines ship Marco Polo. Over the years I have payed so much in single supplements that I now only go on cruises with no single supplement or a very low one. Happy cruising
Very few ships these days have dedicated single cabins. Most shipping companies will sell a two bed cabin for single occupancy. Expect to pay 130% to 200% of the per person rate, although sometimes there's no supplement.