Evasion Clause - You and your opponent cannot use moves or items that raise your evasion, such as Double Team or Bright Powder. This clause does not include the use of accuracy-reducing moves, such as Flash.
Focus Slash/Choice Item Clause - You and your opponent are not allowed to use more than one Focus Slash and Choice item (Choice Scarf, Choice Band, Choice Specs) on your team.
Freeze Clause - You and your opponent cannot use any freeze-inducing moves if one pokemon is already frozen on the opponent's team. Since the moves that freeze only have a percentage of a chance of causing it, not many decide to risk a loss or disqualification in this case.
Item Clause - Your and your opponent's team may not hold a double of any item, for example, two pokemon holding Leftovers. You must have unique items on each pokemon.
Legal Clause - None of the pokemon can have non-legit movesets, abilities, 999 in all stats, 255 EVs in all stats, or 31 IVs across the board.
Luck Items Clause - You and your opponent cannot use items that require luck to be activated, such as the Focus Band or Quick Claw.
OHKO Clause - You and your opponent cannot use one-hit knockout moves such as Guillotine.
Self-KO Clause - You and your opponent may not use self-KO moves such as Explosion if you are both using your last remaining pokemon, to avoid causing a draw. Destiny Bond does fall under this clause if the move connects.
Sleep Clause - Only one pokemon on each team can be put to sleep at the same time. For example, if you put your opponent's current pokemon asleep, you cannot use another sleep-inducing move until that pokemon has woken up or fainted. The move Rest does not count towards this clause. If you put to sleep a pokemon with the Natural Cure ability and your opponent switches it out, you can put to sleep that pokemon without breaking the clause.
Soul Dew Clause - Latias and Latios are not allowed to hold the Soul Dew item in this clause. The reason for this is because without the Soul Dew, Latias is classified as OU, but with the item, she is raised into Uber. Latios is Uber, regardless.
Species Clause - You and your opponent cannot use more than one pokemon of the same species. For example, you cannot have two Garchomps on your team or six Magikarps.
Uber Clause - You and your opponent are not allowed to use Ubers in a battle. Refer to the tier listing to see which are in this category.