According to the official USGA Rules of Golf, players may carry fourteen clubs in their bag for a match. Players must start and end with the same fourteen clubs for the entire match and may not switch clubs out during play. To be safe, players in tournaments should count their clubs before every competitive round in order to avoid penalties.
If a mistake is made – and it happens- where you find a 15th club in your bag after starting the first hole, there is a penalty. If the round is match play then the penalty for carrying more than fourteen clubs is loss of hole for as many holes as the excess clubs were carried, up to a maximum of two holes lost. If the round is stroke play two strokes will be added to the score from each hole played with more than fourteen clubs with a maximum of four strokes added.
The penalty was put into place in 1938 by the USGA following a surge in club carrying in the 1920s based on the differences between steel-shafted and hickory shafted clubs. Up to 20-25 clubs were being carried in a match, giving them an advantage with more types of shot-making abilities. For the first 30 years the penalty was in place there was no stroke limit on the penalty. Meaning you could accrue a 36-stroke penalty for carrying an extra club the entire round. That changed in 1968 to the current rule.
The limit forces golfers to become proficient with the clubs they do carry and diversify shot ability with each club.