"Somebody's Watching Me" by Rockwell has this trope as its general theme.
Which led to its use in a 2008-09 series of GEICO commercials (the version used in the commercials is a remix by Mysto and Pizzi), where your money is watching you. With a big bug-eyed stare.
Tom Waits' "What's He Building In There?" from Mule Variations defines this trope, musically; it's never made entirely clear whether the narrator of the song is just an over-paranoid and unstable person fixating on some innocent and harmless (if slightly reclusive and unconventional) neighbour, or whether the neighbour actually is up to something very sinister indeed...
Tin Hat's cover of "Daisy Bell" turns a charming turn-of-the-century love song into a softly-voiced stalker's fantasy.
"Subway Song" by The Cure. Especially if you are a woman and you have to walk anywhere by yourself at night. Turn around.
The track "Faaip di Oiad" on the Tool album Lateralus. It sounds like a desperate, last-ditch final broadcast by someone who has discovered a number of terrifying things: Aliens are here. They've been here for a while. They've infiltrated many areas of the government and military. They have plans for this planet. And they're coming to get me because I know the truth.
The name itself means something like "Voices of your God" in Enochian ("Angelic"). Eep.
The pAper chAse's version-less Ministry and more Penderecki-2 versions, respectively titled It's Out There and it's Gonna Get You (which introduces We Know Where You Sleep) and We Will Make One of Us (one of their most upbeat tracks, leading into the track The House is Alive & The House Is Hungry.)
Even more chilling is that the lyrics are a recording of a former Area 51 employee calling Coast to Coast AM, a radio show hosted at the time by Art Bell. It could be fake, the guy could be a great actor pretending to have vital information so horrific it causes him to break down and sob, and it could have been a satellite error that caused the radio station to go off the air. But we'll never know, will we?
Another Tool song, Lost Keys, seems to fit perfectly with Faaip de Oiad. The instrumentals don't clash, and the lyrics of Lost Keys start just after Faaip de Oiad's cut off.
The Geto Boys' classic song My Mind's Playing Tricks on Me is a very disturbing song of paranoia and Schizophrenia.
When they went to bed that night no one would have believed
That in the morning, light would not be there
The dark hung heavy on the air like the grip of a jealous man
No place was there known to have been spared
Then panic took control of minds and fear hit everyone
The day the light went out of the daytime sky.
Judging from the lyrics, the song "Lost Northern Star" on Tarja's solo album after her falling-out with Nightwish is probably supposed to be about a guardian angel. But when you actuallyhear it, it comes across more like it's about Slender Man.
"The Wilderness Downtown", AKA the music video for "We Used To Wait", might make you slightly worried about your house being under surveillance. This is because it shows you surveillance photos of your house. Seriously.
Mitigated somewhat by it only being Google Earth, but this doesn't make it any less of a Tear Jerker.
And for that matter, "The Bells are Ringing" and "The Statue Got Me High"
The band generally loves this trope. There's at least one example in every album that isn't specifically made for kids - see the band's page for the ever-growing list.
Does the song in PS2's The Thing called After Me by Saliva qualify?
Planetary (Go) by My Chemical Romance begins with 'There might be something outside your window, but you'll just never know'. Actually, the whole album and much of the promotional material are based around this trope.
The ironically titled "Nothing to Fear" by Oingo Boingo: "Hey, baby, let me give you some advice / The Russians are gonna pulverize us in our sleep tonight." And if they don't get you, then Arab terrorists will. And if they don't get you, a lonely old man in a brand-new car will give you candy or ice cream before getting you wired on cocaine and then raping you. And if he doesn't get you, then one of countless other things - Christianity, television, etc. - will just sap your will and warp your mind. Now go to sleep...
Judas Priest's "Night Crawler." A giant carnivorous worm from Hell can slither into your house, and it will see you in the dark.
Electric Eye. You are being closely monitored and documented by a satellite. Always. You cannot see your surveyor watching or even know that it's watching but it's there, and if you do even one thing out of line it will not only see it but it will document it.
Ben Folds' song "From Above" provides the lovely little notion that you have only one true soul mate and you can pass by her/him every day without ever thinking about it. And you'll never truly be happy without him/her.
"Muthufukka" by Beck: "Everyone's out to get you, motherfucker!"
Rammstein's 'Stein um Stein' (which translates to 'stone by stone') starts off relatively unassuming, with the narrator informing someone he's going to build them a house... a house without windows or doors, where 'no light gets in'. Yep, he's going to wall them up and leave them to die. Sweet dreams.
Iron Maiden's "Fear of the Dark" is all about what could be hidden in the darkness...
Eiffel 65's debut album Europop includes a track entitled "Too Much of Heaven." The song's chorus repeatedly says that Heaven can always turn around, and closes with the line, "the killer makes no sound." Who - or more disturbingly, what - is "the killer?"
The Songdrops song "Tarantulas" is about tarantulas and how they could be anywhere, even on your head and how they "don't bite unless [they sense fear], so just stay calm until it's gone in a year." Slightly nullified if you know tarantulas can't hurt humans, but there's still the "if there's just fuzz where your hamster was, it's probably because of tarantulas" line.