The minimum age to sail is one year. There are no formal children's activities available during most sailings, but you'll find an increasing number of family groups onboard summer and holiday sailings, especially when they're shorter than two weeks long. This has led to the addition of Club Mariner children's programs from June through August, as well as during holiday periods. There's a series of (supposedly) age-graded events for kids 5 to 11, and 13 to 17, led by two dedicated youth staff; on our cruise, many of the activities were the same for 5 to 17 year olds, leading at least one teen to deem them "lame."
That said, we were impressed with the number of kids on an August sailing -- many part of multigenerational family groups -- and they were all well behaved and having a great time. We did see some of the younger kids playing games in the Stars Lounge or card room and getting their face painted; the older ones spent most of their onboard time in the pool or playing Ping-Pong. If you're considering bringing kids during these times, don't hesitate; the families we saw were happy and enjoying themselves. If you're nervous about cruising with lots of kids, don't be; the kids on our cruise were very well managed, either by their parents or by the youth staff.
A children's menu is served in the Compass Rose during peak family travel times, with kid favorites like chicken tenders and mac and cheese, though children can order full or half portions off regular menus, as well. In-suite babysitting services ($25 an hour per child, up to two kids) are offered upon request and availability of staff. Inquire at reception with advance notice.