The claw hammer is the most basic hammer. It should be used only for light-duty nailing jobs.
The dead-blow hammer has sand inside its head, which helps protect the work piece. This type of hammer is good for working with furniture and metal, and for taking things apart without damaging the surface.
The ball-peen hammer is used for striking cold chisels and for general metal work. Its small, flat head is good for driving small nails.
The drywall hammer has a curved head for countersinking nails into drywall. The opposite end of the head has a nail pull and a knife for scoring drywall.
The rubber mallet is especially good for woodworking, as it won't damage the surface of wood. The rubber mallet is the best choice for assembling or disassembling furniture.