For most animators, a non-drying, oil-based plastilina product such as Van Aken clay is used. In many circles it is viewed as the standard for clay animation. The beauty of Van Aken clay is that it is pliable, easy to use, and comes in many different colors. It can also be purchased at many craft retailers and is readily available online. A version of Van Aken clay, called Claytoon, is specifically designed to create Claymation characters and comes in multicolored variety packs and project kits which actually include directions about how to create different claymation characters!
Plastilina (wax and oil-based modeling clay) comes in different grades, each of which affects the pliability of the material. If you find products which describe themselves as being a type of plastilina, search for one that is either school grade or amateur grade, as it will most likely have the consistency you need to create your animated world. You can choose to use either wax-based or oil-based clay, but most animators would agree that oil-based clay tends to “keep” better and will not dry or crumble during your shoot.
Another very popular type of clay is polymer clay, which can be shaped and molded but is a bit harder than typical modeling clay. This clay comes in incredible varieties and textures, and can be baked in order to create certain non-moveable elements of your design such as feet and set pieces. A commonly used type of polymer is the Sculpey brand, which can be purchased anywhere plastilina products are sold. Polymer is less likely to suffer from crushing dents while you adjust the poses of your figures, and colors will not tend to bleed onto each other as much as they might with plastilina clay.
Sculpey comes in many forms, even a unique blend that is non-bakeable and as easy to shape as modeling clay. This polymer is called EZ