Clipping the edges off of coins was an extremely common practice when coins were made of valuable metals such as gold or silver. The removal of tiny pieces of metal from each coin that passed through the hands of a clipper would add up, until an amount worth selling as bullion (often back to the mint where the coins had been made) or to a jeweler accumulated. Hand-hammered coins were usually irregular anyway, so it wasn't always obvious when a coin had its edges shaved off. It was usually considered a serious crime; in England in 1270, almost 300 Jews were accused of clipping and beheaded. There were some early attempts to make coins where clipping would be impractical, such as Henry III of England's "long cross" coins with a cross which extended to the edge of the coin to make it visible if some were cut off.

During the reign of Elizabeth I, a man named Eloy Mestrell came up with the idea of using coin-stamping machines to make coins with a milled edge (similar techniques are reeded or grained edges), so that the absence of the texture on the edge would be immediate proof that the coin had been clipped. Established coinmakers didn't take to the idea and forced him out of working for the English mint in 1572 (and he was hanged for counterfeiting six years later). The Frenchman Nicholas Briot had no more luck in the 1620s persuading his colleagues at the Paris Mint. Briot went to England and did produce some English coins in the 1630s, but many more coins were still made with no anti-clipping design. It was another Frenchman, Pierre Blondeau, who persuaded first Louis XIII of France and then Charles II of England of the advantages of the new kind of edge.

However, even though new coins couldn't be clipped, the old clipped coins stayed in circulation in England, because turning them in at the London mint meant that you'd get only the value of the metal, which would be less than the coins' face value. Blondeau estimated that most old English coins were 20% to 30% underweight from clipping; other estimates said 50%. It took until 1695 (and the reign of William and Mary) before government legislation finally required all clipped coins to be turned in.

Other countries adopted anti-clipping measures around 1700; for example, the Spanish milled dollar (better known as the piece of eight) was issued in 1732. Clipping became less and less feasible as advances in coin-making continued.

Sources:
Bernstein, Peter L. The Power of Gold: The History of an Obsession. New York: John Wiley & Sons, 2000.
http://www.tiac.net/users/hcunn/gol-br-feave.html
http://home.att.net/~enrada/bulletins.htm
http://www.jthep-antiquities.co.uk/Information/Coin%20info.html