Preferably in Survival mode, for example, to lead challenges like a nomadic life or stranded on an island:-)
How about the Pacifist Challange? You can't beat or kill a mob, whether it's an animal or a monster. Traps to kill mobs are also not allowed.
The eco-challenge is not bad either.
For every tree that you fall, you have to plant a new one, buildings, tunnels and quarries must not get too big.
Mobs may only be killed in self-defense against this one. What does not attack you must not be killed.