Our 4-day Wonder cruise, the kids were 9, 10, 11 and could sign in/out only from the room to the club and only if they were together.
Our 14day Magic repo cruise, the kids were 10, 11, 12 and we brought along Post-its. The kids had to stick a note with time and where they were going on the big mirror and could only go to the next place if they first came to the room and left another timed note. This way I could always find them. They also knew they were NEVER to go into anyone's room or to allow ANYONE (even the room steward) in. If the room needed to be cleaned, they went up to the basketball court or to the club for that half hour.
This worked REALLY well. They mostly went to the movie theater, shuffleboard, basketball court, club, or just up for icecream and chicken fingers, then back to the room. I did worry and I did constant surveillence, but in two weeks, they never once abused this privelege. It actually was a great learning experience for me (VERY overprotective Mom here).
I would say each parent knows what is right for their family.