The monster of the week is to Horror Games what a Dungeon Crawl is to fantasy games. You know the drill. Kick down the door. Kill the Monster. Take its stuff. In horror games, it goes a little like this. Investigate something strange. Figure out what the monster is. Research/Gear up. Kill the monster. This can get old pretty quickly in a horror game. After facing the same creature a couple of times, the player characters are going to ready and have their anti-monster kits at the ready. While this is pretty much your standard adventure format, you really should to keep the player characters on their toes.
1. Sometimes Killing The Monster Is Just The Beginning: Yeah, you killed it. But that opened up a whole can of worms. Why was it here? Why did it have that mysterious artifact? Why was searching that old church? Why did it target this one family? Make the mystery more important than the monster.
2. Make The Monsters Individuals: They have their own plans, agendas and emotional baggage. Sometimes an evil monster needs love too. Plus not every vampire and werewolf has to have the same weaknesses and strengths. Change it up a bit.
3. It Really Was Old Man Smithers: One instance of this should curtail the more trigger happy player characters. Throw in a well planned hoax in or maybe a real estate scam. It also enforces the old adage, “Don’t assume anything.”
4. Make It Personal: Maybe a player character has grudge against this monster. Or maybe that special someone has been turned into a monster.
5. The One That Got Away: OK, maybe you didn’t kill it. Maybe it had you and your crew against the ropes and could have offed you easily. But it let you go. Does it have bigger plans? Was it just playing with you?
6. The Hunter Becomes The Hunted: The player characters are used to hunting down the monsters and saving a few locals while they are at it. But what if it’s just a trap, tailored to them.
7. The Lesser Of Two Evils: Sometimes the first monster isn’t as bad as what coming next. Unlikely allies in a struggle against a greater evil. It could make for some interesting role playing.
8. It Doesn’t Have To Be A Monster: Sometimes the monster doesn’t have to be a monster. It could be a cursed artifact or some other object. It could a car, a house, a sword or just about anything. Since you really can’t “kill” an object they going to have to come up with some other way to deal with it.
9. Alternate Reality/Time travel: With all sort of supernatural mojo in the world, an occasional time warp or interdimensional rift might the characters in. Sure they might end up in place full of monsters but they really going to worrying about how to get home.
10. No Monster At All: Give the player characters a vacation or let them have a party. You know relax, maybe meet some new contacts or possibly some more enemies. Or just get thrown in jail for public intoxication. Let them have fun.
Chuck on 
Banesfinger on 
One of the best ways to avoid “Monster of the Week” syndrome is to take the monsters out of the equation for a couple of sessions. Let them fight against purely human evil for a couple of nights. This can also tie itself to your point #3 above — if your players are expecting a monster, and instead end up killing a human (innocent or otherwise) they’re suddenly in a very different situation.
Of course, if you’ve tried removing ‘Monster’ from “Monster of the Week” and still are stuck in that rut, remove the other half of that name! Stretch things out — make the monster extremely cunning and extremely hard to find. And definitely don’t tell them what it is before they face it for the first time; that ruins the suspense.
All great points and good advice.
Also, falling under the Make The Monsters Individuals would be make a monster act like another.
The TV series Supernatural features examples for all of those (though I can’t recall any for 1 or 10 right off):
2. Since they were all once humans, pretty much all the ghosts could fit in this category.
3. Hell House started out like this. And while a ghost was involved in The Usual Suspects, the actual killings were done by a corrupt cop covering up his misdeeds.
4. The major premise of the first two seasons.
5. Something Wicked resulted from one of these. Tall Tales also counts as one.
6. Happens so many times there’s no point in naming a specific episode.
7. Bloodlust
8. Bugs, Croatoan.
9. What is and What Should Never Be, Mystery Spot.
Does it show that much that I’m a big Supernatural fan? :)