Purple Coins are coins found in Super Mario Galaxy and Super Mario Galaxy 2. They appear when there is a chance of a Purple Comet appearing at any galaxy with a Purple Comet Star. For each of these, the requirement is to collect 100 Purple Coins. In Super Mario Galaxy, the Purple Comets start appearing after Mario beats the game.
There are two main variations on the Purple Coin Star: the first is the collection of 100 coins of which there are only 100, it can either have or without a time limit. The second is timed, but there are more than 100 of the coins, generally around 150.
Purple Coins reappear in Super Mario Galaxy 2 when a Purple Comet orbits a galaxy. Their missions are identical to those from Super Mario Galaxy; 100 Purple Coins must be collected to get a Power Star. Purple Coins are worth 5 gold coins.
Purple Coins appear in Super Mario Galaxy after you've beaten the game (with the exception of one available in Gateway Galaxy.) They appear again in the sequel, but this time, they appear during the game rather than after the game.