There are kids' clubs in some of the resorts (Polynesian, Grand Floridian, Wilderness Lodge, Animal Kingdom Lodge, Beach Club). They are for kids 3-12, but if you have a child on the younger side of that, know that they require the child to be completely potty-trained - no pull-ups - and bathroom independent. We took our kids to the Sandcastle Club at Beach Club Resort and they had a great time. The clubs open about 4 or 4:30, and the cost is $11.50 per child per hour and dinner is included. While ours were at SC, we had dinner on the Boardwalk and went into Epcot to wander World Showcase by ourselves and watch Illuminations. You do not have to be staying on-site to use the kids' clubs, but you should make a reservation. The clubs have all manner of games, movies and such for the kids to play and several CMs to play with them.
There are in-room baby-sitting services that are not owned by Disney, but are recommended. One is Kids Nite Out and another is Fairy Godmothers. Those babysitters will come to your room or resort and will keep any age, I suppose. They can't take your children to the pool or give them baths, but can take them to the resort food court for dinner (you provide funds), and watch the poolside movie.
