Official Hallowed Competitive Fantasy Battling Tiers
Uber Tier
OU Tier
UU Tier (anything not listed in Uber or OU)

Species Clause - A player cannot have more than one Pokemon with the same National Pokédex number on a team. For example, using two Beedrill on the same team is not allowed.
Evasion Clause - A Pokemon may not have the moves Double Team or Minimize in its moveset.
Sleep Clause - You lose if, at the end of your turn, two of your opponent's Pokemon were put to sleep by a move you used but were not forced into, and neither have had their sleep removed since then. Rest does not count towards this rule.
OHKO Clause - A Pokemon may not have the moves Fissure, Guillotine, Horn Drill, or Sheer Cold in its moveset.
Swagger Clause - A Pokemon may not have the move Swagger in its moveset.
Endless Battle Clause - Players cannot intentionally prevent an opponent from being able to end the game without forfeiting. For example, a Slowbro holding a Leppa Berry can create an endless battle using the moves Recycle, Heal Pulse, Slack Off, and Block. To do so, Slowbro traps one of the opponent's Pokemon, PP stalls it, and heals Struggle damage indefinitely using Heal Pulse and Slack Off.

Tiers - You may only use Pokemon from the same tier and tiers below the Tournament/Gym's listed tier. For example, if a Tournament is an OU Tournament you cannot use Uber Pokemon but can use Pokemon from all tiers below it.
Levels - You may not use Pokemon over the Tournament/Gym's listed level cap and all of your Pokemon must have leveling disabled, unless stated otherwise.
Items - You are not allowed to use any restoration items during battle, such as Potions and Revives. You may use held items such as Life Orbs, however.
Disconnecting - Disconnecting mid-match during an official battle will result in a forfeit, unless ruled otherwise by a Tournament Official or Gym Leader. Disconnecting mid match will result in a forfeit.
Pre-Battle - Your Pokemon are not allowed to have a status before the start of your battle. For example, they can't be poisoned, burned or have any other status before you begin your battle.