Dave's Stupid Rule is a regulation that is in effect at most tournaments. While there are minor variations of the rule, they all have the same intention: to prevent a player from having an unfair advantage by playing the same stage multiple times in a match. The rule is named after the smasher Scamp.
At the rule's simplest level, no stage that has already been played in a round may be picked for another game in the same round. For example, a random pick chooses Final Destination for the first game of a Falco vs. Ike match. The Falco player loses, so s/he gets to pick the next stage. S/he wants Final Destination again, because it's a good stage for Falco. However, Dave's Stupid Rule states that Final Destination cannot be played again in that round, so the Falco player must pick a new stage.
The most common variation of Dave's Stupid Rule is that a player cannot pick a stage he or she has won on during the round in question. Therefore, under this variation, the Falco player would be free to pick Final Destination for the second game. However, imagine that Final Destination was the randomly selected neutral stage. The Falco player wins, so the Ike player counterpicks Battlefield. Ike wins game two. Now, the Falco player gets to pick the next stage, but because s/he won on Final Destination, s/he can't pick it again.
Another variation says that if the player counterpicking chooses random for the stage, a stage may be played twice. In some tournaments, where only three or four stages are allowed, this is often a viable strategy to get the same stage twice in one match.