The entire grim setting of the game. The Earth's environment has been destroyed, and the only hope of survival lies in Judge Dredd-esque mega-cities where the Police Are Useless and not so different to the criminals they go up against, Fantastic Racism towards androids and human-alien hybrids who mean no harm is commonplace and actually semi-supported by the government, crime is prevalent and three major criminal syndicates are waging war with each other, crazy cults hailing the end of the world are popping up, Total Recall-stype Private Military Contractors are supressing the rights of off-planet miners, and two not so different political parties are waging an all-out "with us or against us" war. The main populace have been manipulated and dumbed down to the point of which they don't seem to know how to get anywhere without the aid of a taxi, and just to top off the nightmare, an Alien Invasion of borderline-eldritch horrors from Another Dimension is occurring. X-COM, which is still (generally) on the side of good, has now become another corporation with a willingness (and sometimes NEED) to bribe and attack other corporations and even the lower populace, and even allow massive wide-scale destruction by gigantic alien monsters so as to exploit the Monster Protection Racket. Even if you win you see the war has apparently taken a massive toll on Mega-Primus, with much of the city being scorched and the cutscene showing a charred MegaPol station still smoking (with one character even audibly noting that "that's good, the fires are under control"). It's also unclear whether the team that was sent through to the Alien Dimension for the final mission actually survived the trip back home too, as their Annihilator crash-lands on a strip of blasted highway after a narrow escape, and there's a fade to black after the final message.
Just to show how evil these guys are, they've enslaved the few remaining Sectoids and use them as a food source.
The revelation of their true motives - all the aliens you've been fighting, believing they were being led by a higher-ranking alien group to conquer Earth? Turns out, they're all just a bunch of (presumably) genetically engineered meat robots for the Micronoids - microscopic parasites that, once injected into a victim's bloodstream by either a Brainsucker or Micronoid Aggregate, take control and put them under the command of their Hive Mind. Once they get inside a host, they automatically gain all the knowledge, memories and abilities of their victims, similar to the X. And they've specifically chosen humans as their new preferred hosts.
The game's soundtrack in general is frightening beyond words. With the exception of some action-orientated pieces of Awesome Music, a lot of the tracks are Nothing Is Scarier incarnate, and wouldn't seem out of place in a Metroid or Dead Space game.
The very first track that greets you when you start up the game, "Alien Beginnings", sets up the mood pretty well. The entire track just bleeds Nothing Is Scarier, with the creepy futuristic bass and odd noises capable of giving anyone who doesn't know what they're going into chills.
"Unseen Enemies" isn't much better. The bass almost sounds like the wind, blowing through the post-apocalyptic land, and towards the end of the track, you hear something that sounds almost like footsteps and a door being opened...
The primary Cityscape theme, "Dawn Over Barrier Walls", is a dark, sinister piece that sounds a little like Laura Palmer's theme, and can make you think about the conditions people are being put through in the game's post-apocalyptic Crapsack World.
"The Cult" is a short, sinister piece of string music that comes crashing down towards the end.
"Hidden Saviors" is a slow, repeating track that sounds just ... off.
"Empty Night Streets" is a empty, droning piece of music that really does sound like something you'd expect to hear down a empty street in the dead of night.
"Shadows". Out of context, you'd expect this track to be straight from Silent Hill or something, what with the ominous droning and the heartbeat towards the end.
"The Infestation" has not only the standard unnerving ambience, but also some borderline alien sounds, like you're actually walking into a building infested by the aliens and their disgusting Organic Technology.
If you ever get caught in the middle of a desert, make sure you have "The Chrysalis Grows" on your phone or iPod. The track is so cold, you'll probably survive the heatstroke.
The Game Over cutscene. You thought the original UFO Defense's one was bad? Apocalypse's game over is quite possibly WORSE, first showing a shadowed alien with ambient sound effects, before showing several explosions on Earth, ending with the planet getting distorted and fading out. At least in UFO Defense and Terror from the Deep, Earth continues to exist (but poisoned), here, the planet is straight-up removed from our universe.