The main types of fossil types are: tracks & trails trace fossils molds & casts coprolites and bones.
First the definition of fossil according to dictionary.com is the remains impression or trace of a living thing of a former geologic age as a skeleton footprint etc. Generally any type living creature can become fossilized over the course of geologic time.
Typically when we think of we think of shells or corals or dinosaur bones which have been buried and preserved in geologic strata. However fossils are not limited to the skeletal remains. Other types of fossils include: