I am the lone stander here!
Of course, much varies by child.
When we went on Carnival Dream, my daughter had just turned 4 and my son was 2.5. They fell in love with cruising. Granted, when we did that cruise, we brought along their nanny. We had a cabin for us and a cabin for the 3 of them. It made life a whole lot easier for us, but we were intent to try it on our own to see if we could cruise with our children (without a caregiver) and still enjoy our holiday.
The following year, when we sailed Eurodam, my daughter had just turned 5 and my sun was 3.5. They had a blast. This was their second cruise. Since then, they have been on another 2 cruises. They love cruising, they love the MDR, they loved formal nights, they love the shows.
Now, I have great kids who are well-behaved and very mature, and my experience is that 3.5 is not too young for a cruise. And I am very lucky in that whether on a cruise, in an airport, church or a restaurant, strangers are always complementing me on how well-behaved my kids are.
The one caution about kid's clubs is that all kid's clubs are not created equally. My kid's HATED camp carnival. At 2.5, my son had never been to daycare, so it was unreasonable for us to expect that he might love being at the kid's club without us. By our next cruise (Eurodam), he was 3.5 and he loved it, and was always begging to go. I think parents need to be prepared for the possibility that their children may not want to go to the kid's club and if that will ruin one's holiday, then they should be prepared to leave their kids at home. For us, we enjoy spending time with our kids, and there is plenty for a family to do together on a cruiseship.
I would not want someone in the family cruising section to read this and potentially be turned off of cruising with young children. If that is what happens, then I think this thread may be doing a disservice to the members of this site. Today's cruises are designed for families, and families with young kids. Cruising is our preferred vacation option, with or without the children.
Parent know their children best and are in the best position to decide whether their children are ready to cruise. There are no blanket age groups to determine a good age or a bad age for cruising.