Red Coins are, as the name says, red-colored Coins. These coins are not just red coins, though. Red Coins are special coins that could give special things when all are collected. Most of the time, there are eight Red Coins scattered around a course. When collected, a Power Star appears somewhere.
There are also Red coins that only appear when a Red Ring is touched. These are rather closer than the normal ones, and also disappear after a small time. Also, when all eight collected, a Power-Up item appears, or a 1-Up Mushroom.