Originally Posted by Bodhisattva

YOU MUST NICKNAME YOUR POKEMON.

The most basic Nuzlocke rules, as they were first introduced, are as follows:
Any Pokémon that faints is considered dead, and must be released or put in the Pokémon Storage System permanently.
The player may only catch the first Pokémon encountered in each area, and none else. If the first Pokémon encountered faints or flees, there are no second chances. If the first encounter in the area is a Double Battle in dark grass, the player may choose which of the two Pokémon they would like to catch.
While not exactly a definite rule, the general consensus is that players must also nickname all of their Pokémon, for the sake of forming stronger emotional bonds.
Also not a definite rule, but the general consensus is that a black out/white out is considered to be "game over", even if there are Pokémon left in the PC.
Strongly implied, though not explicitly mentioned in the comic, is the stipulation that the player can use only Pokémon they have captured themselves, meaning traded Pokémon, mystery gifts, etc., are prohibited. Trading and retrading the same Pokémon (for the purpose of evolving a Graveler, for example) is something of a gray area, and may fall under optional rules. As of White: Hard-Mode Episode 3, it is implied that the player can accept Pokémon that are received freely from NPCs.
Also strongly implied is a prohibition against voluntarily resetting and reloading the game when things go wrong. Being able to do so would render all of the other rules pointless.

hough the above rules tend to stay consistent with all challengers, many optional variations and amendments to the rules also exist to further adjust difficulty. These include, but are not limited to:
Starter Pokémon is based on the player's Trainer ID number. If the last number is 1-3 the player starts with a Grass type, 4-6 is Fire type, 7-9 is Water type, 0 is the player's choice.
Species/Dupes Clause: Adjusting the first encounter rule to prevent the player from having to catch multiple of the same Pokémon, for the sake of variety. Generally this means that the trainer can keep fighting Pokémon in the area until one is encountered that has not been caught yet, which then immediately counts as the first encounter.
As an extension, setting a limit on how much Dupes Clause can trigger in an area. If that limit is reached, no Pokémon can be caught in that area (alternatively; the trainer has to settle for the last allowed duplicate to trigger the clause).
Not officially enforcing the rules until the player has Poké Balls and can catch Pokémon. For example, the PoochyenaRS/ZigzagoonE that the player has to save Professor Birch from is not counted as the first encounter on the route, and not counting any other encounters as such until they can catch. Likewise, in the games where the rival battle is immediately after getting the starter Pokémon, the "any that faint must be released" rule is not enforced at that time.
Use the same amount of Pokémon as the opponent during a Gym battle or rival battle.
Going to options and making the battle style "set", leaving the player unable to switch out.
Releasing the starter Pokémon after the first wild Pokémon has been caught.
Banning the use of Potions and healing items, relying only on Pokémon Centers for healing.
Banning the use of Pokémon Centers, relying only on Potions and healing items for healing.
Limiting Pokémon Center visits to a certain number per town.
Banning the use of held items.
Limiting the number of Poké Balls to purchase per Poké Mart.
Banning the use of Master Balls.
Rather than releasing the Pokémon, it can be permanently boxed, migrated, or transferred with Poké Transfer should it happen to faint.
The player may not evolve captured Pokémon, but evolved Pokémon may be caught.
Turning the difficulty on to Challenge Mode if playing Black 2 and White 2, which increases the levels of opposing Trainers.
No catching/using Legendary Pokémon.
As a mercy rule, allowing 1-3 "second chances" or revives of fallen team members.
As another mercy rule, if the player runs into a Shiny Pokémon, the player may still catch it, regardless of whether or not it is the first encounter in the area. It also does not need to be released if it faints. This is often called the Shiny Clause.
As another mercy rule, each Gym Badge acts as a checkpoint. If the player gets a game over, they can start from when they got their previous Gym Badge.
If the player has no Pokémon that can use a certain field move that is required to continue through any given point of the game, they may catch another Pokémon that can learn said field move. However, it cannot be used in battle for any reason, and must be released, permanently boxed, or migrated as soon as the player gets another Pokémon that can use said field move.
Modifying the "first encounter only" rule for the Safari Zone, sometimes allowing one encounter for each area, or until they catch one Pokémon in the entire area, and vice versa.
Banning the use of Poké Marts.
Disallow fleeing.
Setting a level limit based on the next Gym Leader's/Champion's highest leveled Pokémon. What must happen to any team members that surpass that limit before taking on the Gym Leader or Elite Four is up to the player.
Banning Poké Balls entirely, any Pokémon obtained must be either given to the player or hatched from an Egg.
Banning use of the day care to breed or level up Pokémon.
Turning off the Exp. Share.
Banning use of certain features that make the game easier, such as Pokémon-Amie, the DexNav, or Super Training.
Many other rules exist; challengers adjust their personal rules according to their own preferences. In order to be considered a true Nuzlocke Challenge, however, the core rules must be in place.