But one thing I've noticed that seems to be overlooked by many. It's not just the GM's responsibility to make it successful. As players you have a chunk of that weighing on your shoulders as well and if you don't, well then you may very well be one of the problems.
So here is a short list, and most likely incomplete, of what the players should be doing or not doing.
Help keep the mood. A good GM will set the overall mood of the game. Using a mix of description, maybe some lighting and overall feel he dresses the stage. You need to help keep that stage dressing up. Keep the Monty Python jokes to yourself, stop interrupting for nonsensical reasons and keep the flow going. Shy away from that discussion you are dying to have about the latest episode of the Flash or everything that is wrong with the new Star Wars movie. Focusing on things out of the game yanks others right out of the mindset necessary.
Pay attention (more than usual). Horror games tend to be a lot more descriptive than a lot of other genres. So when the person running the game is describing the something a player has ran across then you need to listen. Then if you run across it later he doesn't need to repeat the details all over again. Repetition of flavor text can really cause some boredom and wandering minds.
If horror is not your thing at all then don't play. Really this should be a no brainer. But if you completely dislike horror then you shouldn't be playing in a horror game. Whether consciously or not your attitude and general feeling will slowly creep over the group like a wet blanket. There are plenty of other games and groups out there, go looking.
Feedback. Let the GM know when things are really working either by your excitement in the game during a break or talking to them afterward. This way he or she really can get a gauge on what to amp up or tone down. Sometimes that vision of a great game can get a little blurry behind the screen. So the more you can shine a light on the sweet spots or the areas that are bit to much into creepyville then the whole group will benefit.