Not all ships have public laundry rooms...you'll want to check and see if the one you are going on does. Some people have suggested steamers....you might even try to hang your clothes in the bathroom while you shower - that sometimes helps.
All the ships I've been on have irons in the laundry rooms, and laundry rooms were easy enough to find, even if not on your floor, just one floor up or down. Very inexpensive to do a load too - just like $1.00 or so - normal laundry room prices.
On days at sea, the laundry room can get VERY busy....once my husband & I waited a considerable amount of time because we really needed to wash some stuff.. after that, I would rather overpack and not have to spend my vacation time doing that...
8/92 Mex. Riv. Commodore
9/98, 9/00, 9/02 & 7/04 Caribbean - Paradise
10/00, 08/05 Pac. Wtrs. Holiday, Monarch
04/06 Hawaii - Celebrity Summit
09/07 Alaska - Celebrity Summit
07/09 Western Caribbean RCCL Liberty of the Seas