Browser-based online RPG Dungeon Empires is now out of beta, though as a free-to-play game, this is a fairly fine distinction. Here's a bit on how the game allows players to assume the role of dungeon master to create challenges for other players:

Dungeon Empires offers lots of possibilities for creating spaces. Players can choose from a variety of room styles, fixtures and elements to that their creatures feel at home in their dungeon. From giant rats, skeletons and trolls all the way to huge dragons, each creature needs its master's attention. If the creatures are well-cared for, they will repay the favor with increased motivation and effectivity.

Players also create their own hero to raid other players' dungeons. The focus can be placed on strength, dexterity or magic. With each increase in level, the hero will receive stat points that can be invested in skills and spells. The hero license system is a special highlight. Players can create a license for their hero and send it to friends so that they can take the player's hero out on raids with them.