In Ancient Greek tradition, coins would be placed over the eyes of the dead so they would be able to pay the toll to Charon, ferryman of the River Styx. Occasionally the coins would be placed in the mouth instead.
This tradition persists in many other cultures today, such as Irish and modern day Egyptian and Greek burial rites. Though there are culturally relevant explanations for each of these, the earliest known occurrences were in Greece, prior to the rise of Rome. In fact, this was one tradition that Roman culture adopted after it conquered Greece, along with much of its pantheon and many of its festivals.