Here is a link to a laundry price list from RCI.
Sorry, the link seems to be working very weird, you have to save it to your computer and then open it (maybe as it is a PDF?), you can't just open it directly (at least I can't).
As Donna said, there are sometimes "wash and fold" days with specials for laundry.
I can understand that it would be convenient to have self service laundry if you for example have kids, but I prefer the laundry service. Even if there are a couple of sea days during a cruise I usually don't have time to do the laundry myself (too much to do onboard and why waste time in a laundry room...