Possession is Nine-Tenths of the Law
No game is complete without bad guys. There are all sorts to choose from, from mafia dons and Nazi generals to orcs and dragons. But what about the original bad guys? The first opposition to the just and the good. They are insidious temptors, and serpent-tongued deal-makers. They are the bargainers at the crossroads, and the twisted souls of the damned. Just as often, they are bat-winged, monstrous soldiers of an eternal war against Heaven. They are Baatezu or Taanari, Devils, Djinn, Pit Fiends, Balors, and Balrogs. Or you could just call them demons: most people would.
Where the Wild Things Are
A demon can occupy essentially any part of a villainous hierarchy in a traditional fantasy game: it can be the power behind the scenes, the apocalypse the PCs are trying to prevent, or just another foot soldier in the service of some larger evil. The vast variety of supernatural threats available in this kind of setting can even leach demons of some of their, well, magic: sure, they are unequivocally evil, but so are a lot of other things! Honestly, as a GM you're a little spoiled for choice when it comes to these guys (or gals, or sexless monstrosities, or whatever).
Consequently, including demons in your in-game cosmology will have the greatest effect if paranormal threats are understood to be at least relatively rare in your game world, if not outright impossible. (Though there's certainly something to be said for a monster-of-the-week gorefest like the CW's excellent Supernatural). In any case, it's probably best not to jump right to Night on Bald Mountain, and instead start with something a little more subtle, particularly if you're playing in a game setting that is meant to be a reasonable facsimile of the real world.
Windows to the World
The thing that really set demons apart from other mooks and villains is that -- in most modern cosmologies, at least -- they cannot directly affect the material world. Demons need agents, willing or not, who can serve as windows (and sometimes doorways) to creation, as they essentially barred from wreaking havoc directly. This author is of the opinion that there's a seed for a really interesting mystery/horror game lurking around the real reason for why demonic possession is so exceedingly rare, particularly if one assumes for the sake of argument that it is a real phenomenon. There's certainly been no shortage of historical effort to understand the literally arcane laws that govern the activities of demons and other infernal spirits, ranging from the more esoteric parts of the Jewish Kabbalah to neopagan spiritualism and secular pseudo-scientific Ultraterrestrialism. Regardless, it's clear that someone or something is keeping a ravening horde of hellspawn from launching a massive assault on reality.
Or maybe not.
Legion, For We Are Many
Something apparently attacked and possessed man in Saskatoon, Saskatchewan (in Canada, for the geography-challenged) in late March 2012, ultimately drawing the attention of a local Catholic priest who had to bless the man repeatedly before he could be taken for formal psychiatric evaluation by local police. According to CBC news,
At the home, the priest encountered a shirtless middle-aged man, slouched on a couch and holding his head in his hands. The man had used a sharp instrument to carve the word "Hell" on his chest. When the priest entered the room, the man spoke in the third person, saying "He belongs to me. Get out of here," using a strange voice. Bishop Don Bolen explained that... it was not clear if the Saskatoon man was possessed or experiencing a mental breakdown. [However], Church leaders in Saskatoon have been considering whether Saskatoon needs a trained exorcist.
Half a world away, Islamic religious leaders in Egypt revealed two weeks later that an 18-year-old girl named Dawa'a had been attacked by a "tribe" of 1,000 djinn. The attack caused Dawa'a to convulse violently and shed tears of blood, though a local Imam insisted that Dawa'a had managed to avoid being possessed completely. Amr al-Laithi, an Islamic scholar, supposedly banished the jinn by "reciting verses from the Quran as the teenager fell unconscious," and later claimed that it was clear that the djinn had never fully entered Dawa'a, as there was "no change in her voice."
The same day Dawa'a was apparently being attacked by demons, two large seismic events struck western Mexico, only to be followed two weeks later by three more. It would be easy to dismiss the potential occult significance of these tremors if they couldn't be linked to any other events of a paranormal bent. But they can. Within 24 hours of the most recent quakes, a rare white Buffalo calf, considered sacred by a number of Native American tribes, was found killed and mutilated on a Texas ranch, very possibly by agents of the same evil entities causing the wave of (attempted) possessions worldwide.
Consequently, it's easy to cast the earthquakes as symptoms of some larger battle in the spirit world, a war for the fate of reality itself. There are a host of potential esoteric explanations for the apparently brewing battle between good and evil, and tons of space to insert a few stalwart PCs or innocent occult investigators.
The war has started. Who's winning?