Full laundry and ironing (pressing) are now widely available aboard all major ships, some will also offer dry-cleaning facilities, all of this at a cost. A detailed list of options will be in your cabin - your steward will collect the items and deliver your clothes back to your cabin.
Very few ships have the option of self-service launderettes. In these cases, they will be well equipped with washers, dryers and ironing facilities. There may be a charge for using these facilities and the washing powder. Don’t expect to find an iron in your cabin, most ships consider them as a fire hazard, nor will you be allowed your own iron on-board.
The cruise lines that offer launderettes are: AIDA Cruises, Carnival Cruise Line, Holland America Line, Princess Cruises and Cunard. Double-check with the cruise line if the specific ship you are travelling on does provide a self-service laundry facility.