What things make a Pokemon Shiny, and what are they?

And all the combinations that lead to Shiny Pokemon.

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Generation II

Generations III, IV, and V

Bulpapedia

However, Victini, Zekrom, and Reshiram, or any Pokemon from the Dream World cannot be shiny unless you cheat

In Generation II, Shininess is determined by the IVs of a Pokémon. If a Pokémon’s Speed, Defense, and Special IVs are 10, and its Attack IV is 2, 3, 6, 7, 10, 11, 14 or 15, it will be Shiny. This determination allowed for compatibility with Generation I, as if a Shiny Pokémon is traded back, then traded forward, it would retain its Shininess.

Generations III, IV, and VIn Generation III, most of the data structures were redone. As such, a Pokémon’s Shininess would no longer need to be linked to its stats due to incompatibilities between the previous generations. The determinant for Shininess is instead a calculation based on the Trainer ID number and secret ID number of the player encountering it and the personality value of the Pokémon. The same method is used in Generations IV and V.

Source:http://bulbapedia.bulbagarden.net/wiki/Shiny_Pokémon