In the age of discovery when the Europeans made contact with indigenous populations it largely resulted in deaths from diseases like small pox which they had no immunity to. Especially in the cases of the Caribbean and the Andean civilizations. In the case of Mesoamerica though the disease that was said to have decimated the populations there was called cocoliztli. Some people have argued that was brought about when Cortes conquered the Aztecs but there are other arguments that it was actually a disease indigenous to the New World and that it probably brought down the Maya civilization during its classical stage. What are the veracity of these arguments?
There's always room for discussion, but perhaps the section Disease in the Americas from out FAQ will answer your inquiry.