Because everything old is new again when it comes to RPG discourse, I recently saw The Dreaded Discourse™ around horror raise its head. This usually comes in two flavors:
1) Adventure games (especially D&D, but a wide net that potentially describes any game the commenter does not like) are bad at horror.
2) Modern horror is hard to do effectively.
The former argument is predicated on the fact that one needs specialized systems to invoke feelings of horror, while the latter argument is predicated on the fact that modern technology is too much of an equalizer in the struggle of humans vs. the unknown.
Both reflect exceedingly narrow viewpoints.
Issue #1: Adventure Games are Bad at Horror
I will freely admit: adventure games typically aren't built for horror, and aren't often my go-to horror games, but sometimes the lack of tools is liberating. Indie games tend to have very specialized procedures as to how characters interact with horror, and even Call of Cthulhu has a typical encounter loop (see the horror, roll SAN against the horror, fail and freak out or succeed and fight or retreat). But all you really need for horror is a sense of powerlessness, and it takes very little to reinforce that — a single powerful attack from the monster, or a single player attack that the monster no-sells, or even just something the players have never before seen, and suddenly everyone is scattering to regroup and figure out what the hell just happened. Ignore the advice on balanced encounters, and suddenly everything is survival horror.
But you don't even need to go that far. Just start describing a creepy environment, and most players get into the zone. I have absolutely made players fear something far weaker than they just by describing it in a frightening enough manner.
It's a sometimes food, and you don't want to just spring it on a group without some warning, but it's still worth trying at least once.
Issue #2: Modern Horror is Hard to do Effectively
I take much greater offense at this one. Sure, it can be hard to do horror when you're running a spreadsheet of ever-ascending numbers and magical powers, but the modern era is almost uniquely suited for horror tales.
As noted above, horror relies on a sense of powerlessness, even if that sense is transient or only arises from encountering something one has never seen before. (Even in the case of something like Unknown Armies, where the horror comes from responsibility, the "powerlessness" arises from unintended consequences and the sense of spiraling out of control. Powerlessness takes many forms.) The alienation of modern, Westernized society gives us this in spades.
I've heard the argument before that people avoid eras past 1980 because of ubiquitous computers and cell phones and automatic weapons, and I've heard the (admittedly rarer) argument that some avoid the last 100 years or even the 20th century altogether.
You have to watch The Thing, or more importantly, Aliens. Technology is your friend as a horror GM, because it offers a false sense of security. Players always like to assume that they can handle problems because of the tools at their disposal: they have guns, cars, and cell phones. Help is just a phone call away, and they can always get into a car and leave the scene if things get bad.
But remember what happens in Aliens. The marines assume their heavy ordinance will nullify the threat while the tactical sorts coordinate the offensive over cams and comms. But their guns do very little to chew through endless waves of xenomorphs, and all the cameras and communication systems do is let the others watch them die.
Modern horror parties spend most of their time apart, embroiled in research, or working dayjobs, or splitting up to divide tasks more effectively. They rarely sleep in the same building, let alone the same room. And they sometimes encounter things that guns cannot put down.
Use this to your advantage.
If your buddies are halfway across the city when you get attacked by the rampaging monster, all your panicked cell phone call will do is let them hear your last, desperate moments. If you manage to get cell phone video of it, amateur digital analysts on Reddit will pick it apart and tell the survivors how fake it looks. Even with the fruits of 10,000 years of human civilization, your toys will not save you.
Everyone dies alone.