RCCL ships do not have laundry facilities onboard. Showers do have a retractable clothes line in them so you can hand wash items and let them dry.
Take a hard look at what you are packing. Most people (ourselves included) take things that they never end up wearing.
Radiance of the Seas - Nov 2006
Legend of the Seas - Jun 2007
Costa Fortuna - Mar 2008
Legend of the Seas - Oct 2008
Celebrity Constellation - July 2009
MSC Orchestra - Jan 2009
Navigator of the Seas - March 2009
MSC Poesia - November 2009
Jewel of the Seas - June 2010