No irons in the cabins and the cruise lines do not want people to bring them on board. They can be a fire hazard. The most logical place to iron your clothes is on the bed. It's the most common place to leave the iron.
Packing clothes in dry cleaning bags, Downy Wrinkle Release and placing in the shower do wonders for keeping clothes from wrinkling or removing wrinkles. Also, pressing services are available on the ship.
This usually becomes somewhat of a hot topic on the boards, regarding bringing travel irons on board or not. As I said earlier, cruise lines do want people to bring them on board but some folks do. My wife and I have never had a need.
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Mike has told you some great options and a couple more is use the iron that the ship provides in th laundry room. No, they cannot be taken to your room as they are permanantly attached to the wall. You can also bring a steamer to steam out wrinkles or finally you can just send them to the ships laundry and they will return them to you very quickly all nicely pressed for a very small fee.
depending upon what ship you are on, you might have a self-serve laundry that has an iron. Look at your deck plans it will tell you. I have used the iron for a quick press of a dress shirt. Everything else i pack in dry cleaner's bags, hang the "good clothes" in the garment bag and unpack and hang up the clothes as soon as i get into my stateroom.
We used to bring a small travel iron which turns itself off after 20 minutes and would iron all the clothes we needed to after our luggage arrived. Then we found the ones in the laundry and stopped bringing it. The steam from the shower works well too.
Book me on your next cruise and enjoy your personal punching bag.