I was at Arlington National Cemetery yesterday. There were many coins scattered over the Kennedy grave. There was a sign asking people NOT to throw coins at the astronaut/Iran hostage rescue memorial....but I think there was grass in front, and those coins would become mowing missiles. At the cemetery on West Point, many of the grave stones have little piles of rocks that have been left on them by visitors.
Leaving a pebble on a gravestone is a Jewish tradition IIRC.