Each Cup has different rules and regulations on things such as levels of the entered Pokémon, moves used, items held, and even the species of the entered Pokémon.
All of the cups have the same basic rules:
The player must enter with six Pokémon. All Pokémon must be different and hold different items. With the exception of the Challenge Cup, the player may select Pokémon from their game pak or rental Pokémon.
The player must select three Pokémon to battle. If the match is won and none of the player's Pokémon faint, a Continue is received.
Eight Trainers must be beaten in a row to win the Cup. If a player loses a battle, a Continue may be used to re-challenge the last opponent.
No two Pokémon can be asleep at the same time. (Pokémon that are put to sleep due to Rest do not count.)
Most of the cups in Pokémon Stadium were based on Pokémon Yellow's Cable Club. The Petit, Poké, and Pika Cups were first introduced in Yellow's Colosseum 2, while the Prime Cup was based on the free battle rules of normal link cable battles.