Whenever I do a nuzlocke, I personally have three difficulties that I do, with some rules I made up:
Classic:
>Must catch first pokemon you encounter each route/area and are not allowed to retry.
>Pokemon that faint are "dead" and cannot be used again, and are permanently boxed in "Heaven."
>Rare Candies, Revives, and healing items are banned from use.
Casual:
>Must catch first pokemon on each new route/area.
>Are allowed to skip catching that pokemon if you have caught it before/in the same evolution line.
>Healing items are allowed.
>Pokemon that faint are sent to Heaven and aren't allowed to be used again.
>Allowed to keep a non-combative Pokemon for HM use.
>Allowed to catch shiny Pokemon
Easy:
>Must catch first pokemon on each new route/area.
>Allowed to skip catching it if you have caught it before/in the same evolution line.
>Healing Items and Rare Candies are allowed
>If you have found a Revive (not bought one), using 2, or one Max Revive, you may resurrect a Pokemon from Heaven. However, if that Pokemon is defeated again, you must send it to burn in Hell and you are not allowed to use it again.
>Allowed to keep a non-combative Pokemon for HM use
>Allowed to catch shiny Pokemon
>Allowed to Save and retry
What rules do you have for any game modes that you use?
>have fun
that's it
Some additional rules I play with:
> you can use only one item per battle
> additionally you can use the same item your opponent used
> you are not asked to switch your pokemon after you defeat one (dont know how it's called in english)
> you can keep any pokemon you get through story (like lucario in XY)
> you cannot have pokemon with same types in team (exception is normal type)
hardcore:
> you can only use items found in the overworld (exception are pokeballs)
> rule of two: you can catch the first two pokemon of a route, BUT if any of those dies, the pokemon you used to catch it dies two (eg. you catch X with Y and catch Z with W, if X dies, Y does too, same goes for Z and W)