Insanity is a slippery subject. It is often heard between vexing party members in the depths of a planning discourse that one will shout "You must be mad!". Now its reasonable to be prone to a little exaggeration in the heat of an argument and I have heard my fair share of 'crazy' plans but it is never wise to throw caution to the wind in a roleplaying game where medical conditions extend into the supernatural.
Possession has roots in the real world but only as a symptom of delusion, schizophrenia or personality disorder. In an RPG you could argue that exchanging minds entirely is a also a case of possession, though not being nine tenths of the law, would be considered more akin to squatting.
Cthulu is of course a defining RPG in terms of madness management and Mythos exposure can lead to any number of phobias from the lighter end of the scale to wholesale evacuation of any and all faculties. So for those with an interest in the gradual fracturing of a human mind then I suspect most GMs would point you in this direction for a grand tour of the insanities. [Achtung! Cthulu currently running, though not sure of the average sanity rating at the moment..]
I have, before now had the chance to play a psychopath, probably one of my most enjoyable experiences. To be unbound by empathy can really create shocking circumstances but of course being on the one end of the scale gives you the freedom do what you want but the vulnerability of not knowing whether you should be concerned whilst sawing off the limbs of people who are still trying to use them.
Being sensitive to alternative realities can be a problem but often seers and clairvoyants are blessed with enough insight to cope up to the point that they encounter disturbing entities in one of the realms. Whether this characterises madness to is unclear to me; I think not as its a power but is the inability to cope with a supernatural gift actually a mental illness ?
I shall finally touch on Genius. When the cognitive faculties are pushed beyond the norm or augmented with technology do you become an exceptional member of society or are you driven off into the shadows? Either way if you an illness that is being celebrated or an infection that is being quarantined, it may be a case of Hero or Villain.
"Protect and Serve" or "Evil Geniuses for a Better Tomorrow".