I suppose that, as ActiveUnique perhaps implies, the problem appears when key-hunting is the most prominent element of gameplay in a large number of games. So perhaps an idea might be to consider alternative gameplay mechanics.
First of all, the ubiquitous fallback position of action elements--be they shooting, hack-and-slash or whatever--are in most cases probably not a good idea for most horror games: action elements empower the player, which can decrease fear, thus hamstringing a horror game.
That said, action might work if it's risky, or if the game is a roguelike/lite, however.
Puzzles and other logic-based mechanics might work, but I do worry that engaging the player on a logical level might reduce their emotional response--but I'm not sure of that.
One gameplay type that seems as though it might work rather well is stealth: the idea of hiding from and avoiding horrible things seems quite natural. Just look at some of the horror-themed levels of the Thief games.
That's what comes to mind offhand; what other ideas are there?