There are no self serve laundry facilities on board. Also, there are no irons in the staterooms, as that is a fire hazard.
However, on one day of the cruise, I think they may offer an "all you can wash" type of thing. You can just put whatever you want to wash in a laundry bag, and for a flat fee, they will wash it.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)