I like things that make sense in the context of the society, what they are doesn't matter.
My two favourite organisations are a society called the boxers in a comic called fables published by DC and the Psi corps (ok, technically not magic but same principle.)
The boxers are a regiment in an army. The world has magic as an unequal resource with some people having massive amounts of power and most people none. Soldiers with a degree of magical talent were organised to take down major threats, but no one of those soldiers was a major threat alone. Their nickname came from the magical boxes they imprison the unkillable major powers in. Basically the culture was feudal, and people achieved positions according to their power, ambition and ruthlessness, so magic was largely unchecked unless a local mob picked up pitchforks, someone more powerful wanted your stuff or the central Empire noticed you'd stepped too far out of line.
Psi corps was enjoyably creepy. The population had such a great fear of telepaths that everyone had to be registered, monitored and trained, or take medication to restrict their ability. The most powerful telepaths were groomed and persuaded to join the psi cops, and psi cops policed the psi corps. If you then happen to have a morally dubious git with a superiority complex (like Alfred Bester) at the head of the organisation you have no protection from your protectors.
Most societies would have more than one organisation though. Take the x-men universe. Prox X founds the xmen to protect people from Magneto and other evil mutants. Simultaneously the government is building giant mutant-hunting robots, vigilante groups try to run mutants out of their neighbourhooods and various scientists try to find ways to track, depower, sterilise or imprison mutants for the good of humanity.
For me, the richness of the lore and the understanding of why that society has tried to protect itself from "power" in that particular way is the draw.
Craig