Basically playing through the game in 'hard mode'. Two main rules:
1. If a pokémon faints, it is considered dead and must be released. It can't be used again.
2. You can only catch the first thing you see in any new area.
However, I've seen some use a 'duplicate' clause in that if you catch, for example, a Pidgey in one area and the first one you see in a new area is Pidgey, you can catch the next new one (otherwise you could end up with a team full of the same pokémon).
To make it harder as well, some will not use healing items in battle and have a setting changed so that you don't know what the next pokémon is when in a battle (in the games, you're told that your opponent will use a certain pokémon next and if you wish to change. The setting change means that you can't switch beforehand).
I pretty much follow all the above just to make it a little more challenging.