Ancient Anglo-Saxon law punished eavesdroppers, who skulked in the eavesdrip of another's home, with a fine; the eavesdrip was also sometimes called the eavesdrop. Eavesdrop also means a small low visibility hole near the entrance to a building (generally under the eaves) which would allow the occupants to listen in on the conversation of people awaiting admission to the house. Typically this would allow the occupant to be prepared for unfriendly visitors.
Early telephone systems shared party lines which would allow the sharing subscribers to listen to each others conversations. This was a common practise in rural America which resulted in many incidents and feuds.
Eavesdropping can also be done over telephone lines (wiretapping), email, instant messaging, and other methods of communication considered private. (If a message is publicly broadcast, witnessing it does not count as eavesdropping.)
In ancient China, it is said that to prevent eavesdropping when discussing important matters, soldiers would instead draw the characters on hands or papers. This is where the superstition of the "black dot" on a piece of paper comes from.