How many bones do sharks have in their bodies?

Sharks do not have bones.

Sharks use their gills to filter oxygen from the water. They are a special type of fish known as "elasmobranchs", which translates into fish made of cartilaginous tissues. Their cartilaginous skeletons are much lighter than true bone and their large livers are full of low-density oils, both helping them to be buoyant.

Even though sharks don't have bones, they still can fossilize. As most sharks age, they deposit calcium salts in their skeletal cartilage to strengthen it. The dried jaws of a shark appear and feel heavy and solid; much like bone. These same minerals allow most shark skeletal systems to fossilize quite nicely. The teeth have enamel so they show up in the fossil record too.