Disney, Carnival, and Royal Caribbean, MSC and the Norwegian Escape have group babysitting for babies (at least one year old on Royal Caribbean) that costs money and is based on availability.
MSC is is the ONLY cruise line with babycare Service which does provide FREE babysitting for children between 1 and 3 years old during select hours.
On Royal Caribbean and Celebrity you can also pay for stateroom babysitting for kids ages one or older, along with Holland and Princess for kids ages three or older.
There is a nursery available on Norwegian, MSC, Carnival, Cunard and Celebrity with toys and games. Parents are required to be present in this nursery and to change their babies while they are playing in these nurseries.
Costa has group babysitting for kids 3 and up only.