- You can only catch the first Pokemon you find in any area (route, cave, city etc.). If you don't, sucks to be you. You can't catch any more. Even if it's one you already have.
- If a Pokemon faints, it's dead. You have to release it.
- Give all your Pokemon nicknames so you grow attached to them.
This makes the game a hell of a lot more interesting and challenging. And it's not unusual for Pokemon to just die due to sheer bad luck, which is just horrible when you get into it.
Pro tip: ALWAYS have Antidotes on you.
The origin of the word "Nuzlocke" can be found at www.nuzlocke.com. The guy has also done a series of hilarious comics.
I'm currently doing a FireRed run with my Squirtle called Bunk (after Bunk from The Wire). I'm at Vermillion City right now and I've lost just the one Oddish in Diglett Cave. You just don't see Magnitude 10 coming :( RIP Vinny