On the Sun Princess , the washing machines were free but you needed quarters for the soap powder (4 quarters per small box). No coin machine there but you can always get change from the casino I suppose. There is an iron there as well but there are normally queue for that on formal nights. One laundry room on each deck so if the laundry room on your deck is busy try the next deck up or down.
If one feels that the laundry facilities should be better or be free, just remember that they don't even have any laundry facilities on Celebrity ships. When I pointed that out as being a plus for Princess I was scolded that one should not be doing laundry on a cruise but vacationing and that they could always send the clothes out to be laundered. Since we normally take cruises of 14 days or more, we'd like to be able to wash certain items and pack less. I don't like being trapped with paid laundry service the only option.
I also agree with you, even for a 7 day cruise I can pack a little less if I know I can at least do one load of laundry during the week. Its also very nice when you return home and not have 2 suitcases full of dirty laundry, not a nice homecoming when you have a million other things you need to do.
There are laundry rooms on all Princess ships. Some, of course, have more than others. We just finished the Tahitian Princess and she had 2 laundry rooms (well, I know I used one). The Tahitian is the smallest ship in the fleet (650 passengers) and there were 3 each of driers and washers. They cost $1 each to operate. Soap was automatically dispensed.
On the other ships, the machines were free but soap was $1.
There are also laundry and dry cleaning services available at a nominal charge.
If you check the ship plans on the website, you can find where the laundry rooms are. Be prepared. They do get busy.