Sawnee -- The basic reason for this is a bit grim -- the muscles around the eyes could constrict after death, causing a persons eyes to open, scaring the hell out of everyone. Ancient cultures, like the Greeks, came up with legends to account for the tradition of putting coins over the eyes to stop this from happening, like the myth Cord notes that the coins were to pay the ferryman across the river Styx.
Of course coins had more value in those days. Here's a joke my papaw told me when I was about 5-6 that I never forgot. Two old fellas are sitting side by side in a two-holer outhouse when the first guy starts to pull put his pants -- and some coins clatter into the hole. He gets a sorrowful look on his face, then fishes in his wallet for a $5 bill, and throws it in.
His friend says, "What the hell did you do that for?" And the guy answers, "If you think I'm fishing around in there for 35 cents, you are crazy."