It is known as the Nuzlocke Challenge. It works for the various Pokemon games, best with emulators.
The rules are simple.
1. Any Pokemon that faints is considered dead, and must be released.
2. The player may only catch the first Pokemon encountered in each area, and none else. If the first Pokemon encountered faints or flees, there are no second chances.
3. You must nickname the Pokemon you catch.
Now granted there are other extra rules you can add you make it more difficult like limiting Pokémon Center visits to a certain number per town or limiting the number of Poke-Balls to purchase per Poke-Mart, but the three core rules must be followed.
Are you up for the challenge?