From natural processes of the digestive track, dinosaurs have left us with one more valuable clue into their world and that is coprolites.  Coprolites is the fossilized fecal matter of dinosaurs.  It can come in many shapes and sizes and can tell us allot about the animals diet and environment.  From looking at the morphology of the feces one can make an assessment to what type of animal left the feces.  For example, sharks have intestines which are spiraled and thus a spiraled feces is left behind.  The diet can be assessed by looking at the morphology and the mineral content as well.  Herbivorous creatures have coprolites which vary in size and make up a series of droppings and show fossils of plant material.  Carnivorous creatures have coprolites which are usually large and elongate and show fossils of bone material.
 
 

Sauropod coprolite; Morrison Formation Eastern Utah (A.J.Martin)

The preservation of coprolites varies with the conditions present at the time of burial and who the feces was produced by.  Feces from a carnivorous dinosaur is more likely to be fossilized because it contains more mineral content e.g.. calcium phosphate  which can help with fossilization.  Also the fecal deposit form the carnivore is more or less just waste material and is less susceptible to scavenging.  Feces from herbivorous dinosaurs is less likely to be preserved because of its high concentration in partially digested plant material.  This material is highly susceptible to decomposition and scavenging.  The best way for preservation is that the fecal matter partially dries and then is quickly buried.