Take two equally sized coins and keep one fixed. Roll the other along the outside of the the first coin, without slipping, until it has gone all the way around the first coin. That is, the second coin rolls along a distance equal to its circumference.
How many rotations did the second coin make?
2 rotations!
Proof
The easiest way to see this is to first draw a line equal to the coins circumference. It will take the coin one rotation to roll along the length of the line. Now with the start of the line fixed and the coin fixed at the end of the line, curve the line into a circle. The coin will rotate one more during this process.
When the coin rolls along the outside of a circle, both these rotations happen at once: one from rolling and one from traveling along a curve.
Also see the Coin-rotation paradox. page on Wikipedia.