I was running a zombie game..end of the world, survive at all costs type horror game, but it ended before I could introduce a lot of horror elements.
Currently, I am running a modern day horror/shadow creature game (using D20 Modern with Urban Arcana/Weapons Locker/Modern Player's Companion I and II). It's kind of a BtVS/Angel/Constantine/Van Helsing- themed game.
There's demons and other creatures of Shadow constantly hammering their way into our world and of course, there are those folk who would open the door for them and invite them in. Most are simply hunters, animalistic, dangerous but predictable. They come here, kill people, drink their blood, eat their eyes, etc but have no thought beyond the next meal and securing some territory, maybe even breeding if more than one of their kind came through. My PCs are members of the Catholic Church (two priests, one layperson) who secretly combat these menaces. The animalistic predators don't scare them quite as much as the few demons that come from Hell who can plot, plan, and have goals.
I get kind-sorta complaints from one player who says it's too dark, that there seems little hope, and the tone of the game is gritty. We've had one PC, in horror at what he had done under the influence of a very powerful and old demon, commit suicide with a 9mm pistol in front of his fellow PCs; one get possessed and kill a bunch of innocent people; still another that shot a sixteen year old fleeing kid in the back with a shotgun from ten feet away; oh, and one is doing community service stemming from an arrest for obstruction of justice.
The PCs routinely deal with issues like homosexuality (in the "closet" and otherwise) and the Church, moral vs ethical and the law, uses of deadly force (with humans, not demons/Shadows), use of force against the possessed, the homeless poor as victims of society, institutionalized brutality, alcoholism, drugs, suicide, etc
As you can probably guess, I like dark, gritty games. It seems more realisitic and far more interesting than cinematic, "four color" comic book style games.
The players are able to lighten things up with witty banter (inappropriate humor in the face of death ala Angel or Buffy) and concentrating on the more civilian side of the priesthood..two or three confessions a day by lovely old women in the neighborhood, being able to help those in need, sermon topics on Sunday services, etc.