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Nightmare Fuel: X-COM
When "Not Enough Time Units!" comes at the worst possible moment...
Chryssalids are super-fast, heavily armoured aliens (looking very much like a Xenomorph) who sprint across the battlefield at an impossible rate, and in the earlier parts of the game can take the concentrated firepower of an eight-strong squad to bring down (sometimes even that barely hurts them). If they attack one of your team, they will kill them. Then the fun starts. Anyone 'killed' by a Chryssalid becomes a CPU-controlled zombie enemy. They hit hard, but they're slow, and easy to kill. Except... when you kill them, a brand-new, fully-grown Chryssalid bursts out of the corpse. If you're still using the starting weaponry, you might not have even killed the first one when it happens. Some players will go as far as have their troops carry primed grenades in their off-hands when going into a terror site with Chryssalids - if they get zombified, they'll drop the grenade and kill themselves, and maybe soften up the Chryssalid.
The Tentaculats. For one, you only encounter them at Alien Colonies, Artefact Sites and large Submarines. There's a good chance you'll be fighting them in the dark, which adds to the creepy atmosphere all to well. Second, they look like giant tentacled brains with huge octopus-like beaks.
In between turns, you can hear the pitter-patter and slithering of aliens walking around, the occasional weapon blasts, the screams of dying civilians, the opening and closing of doors, the fear that if the game switches to the main view then you will watch a Chryssalid or other enemy suddenly jump out and kill your troopers, the creepy music, and sometimes, total silence. And it doesn't help that the "Alien Turn" image is of a wounded soldier in a picture that is mostly black-and-white except for the red of his blood. Right behind him is what looks like a Muton about to tear him apart with his bare hands.
Discovering the effectiveness of alien grenades and blaster bombs. The hard way. And then trying to organize some kind of retreat with at least half of your whole squad dead in one turn.
Aliens with psionic control, with a squad of troops who have low psi-strength.
Night missions, before you figure out effective night fighting tactics. Your troops get sniped from dark corners, and when you have your troops approach them, they just get cut down by reaction fire.
Terror From the Deep didn't get its name for nothing. Essentially, it's UFO Defense mixed with H.P. Lovecraft. The aliens you fight are the stuff of nightmares, especially the Tentaculats and Lobstermen. To clarify on the latter, the Lobstermen are giant crustaceans that can shrug off any attack that isn't a melee weapon, while tearing your own troops to pieces if you are not prepared.
Many of the aliens in this game indulge in Body Horror. The Deep Ones are humans that were grafted with Aquatoid DNA in the most gruesome way. Bio-Drones are piloted by brains that were butchered into submission, and use a sonic beam based on their original vocal cords to scream their enemies to death.
Chamber of Ultimate Alien is surprisingly creepy. Alien itself resembles huge aquatoid with Cthulhu tentacle face and its in coffin shaped "bath". However, creepies part is that its reanimating process is powered by 8 alien fetuses/babies in glass jar. Which then wriggle in pain while getting electrified after you shoot the glass, which you need to do to kill the Alien.
Also from the reboot, the Thin Men, a modernized version of the Snakemen. Faster, more mobile, and they both spit poison and explode into poison when killed. Good hunting!
Sometimes, due to a glitch in Enemy Unknown, an enemy unit may spontaneously appear next to one of your soldiers as if they teleported from out of nowhere. Bad enough when it is a Muton or Cyberdisk, maybe even a Sectoid, but this can also happen with a Sectopod.
The tutorial mission of the reboot is pretty creepy too. You come across German soldiers, one that's been killed with conventional (for the aliens) weaponry, and one that's been somehow eviscerated when, to use Dr. Vahlen's words, tore its way out of his chest. Then there's a German soldier from inside a building calling "Hilfe..." What does that mean? "Help me."
XCOM (no hyphen)
If you hang around an investigation scene too long, the Sinister Geometry aliens will arrive and vaporize you. It's scarier than it sounds.