1 - If a pokémon faints IT IS DEAD. It must be taken to a pc and released, there are no exceptions to this.
2 - In line with the above rule, if all of your pokémon
faint die its game over.
3 - Nickname your pokémon, making it all the more upsetting when they die.
4 - No out of battle healing AT ALL apart from pokecenters and other such npcs.
5 - You may only catch the first pokémon of each new route/city, new pokemon fainted? Tough shit. Wanted a pokémon that only shows up here but wasn't first? Tough shit.
6 - All legendaries must be killed or caught, stuffed in a box and never used.
7 - Battle Mode must be set to "Set" in the options. (No free switches when enemy switches)
8 - Record your journey, be it through a badly drawn mspaint comic (Which is the traditional medium) or through a story/log.
Optional rules for those who rule:
These are either not accepted by everyone, or are custom rules suggested in this thread and added to the list, pick and choose from these as you like.
9 - You may only have 6 pokémon at a time, if you see and catch one you like when your party is full you must sacrifice one of your current party for it, this is the same as normal death.
10 - You are limited to your first five pokéballs, what you find in the wild, and one bought from each town.
11 - No healing items at all. (replaces rule 4 which allows items to be used inside battles)
12 - No grinding. Improvise.