NCL ships with self service laundrymats are
Dawn, Jewel, Jade, Pearl, and Gem.
The use of the laundry is free, there is a vending machine for the detergent, which isn't that expensive - a buck or two, which you can avoid if you bring your own detergent.
All NCL ships have a ship laundry that provide valet services. Here's a Valet Service order form
NCL usually has a fill a laundry bag special mid way through your cruise for 20 bucks. Don't expect overnight service with the laundry bag special.