This is based on opinion. Please don't list it on a work's trope example list.
Nightmare Fuel / They Might Be Giants
Hide Away Folk Family, especially the coda, which culminates in something not unlike Courage suffering from catatonic shock.
"Rabid Child" from their first album is quite haunting. It starts off with a distorted and warbling voice that says "Lord, please don't take me away..." It also has a music video, which except for one clip, has NEVER been released to the public.
Oh, you know that song "The Statue Got Me High"? The one with the statue that just makes people burst into flames and die? The song mentions it's being displayed publicly.
To add to that, try not to scare yourself with John Linnell's intense stare. Who says statues can't move. And sing.
"Cloissone". The narrator of the song's obviously up to some unsettling activity. "You've got a friend in law enforcement, don't go calling law enforcement..."
"Turtle Songs Of North America," a free download from one of their old sites, consists entirely of weird noises and John Linnell speaking in a creepily calm southern accent about several imagined North American turtles, including the Eastern Fighting Turtle, the Downy Tortuga, and the Mudflail.
"Replicant" from their 2013 album Nanobots. It's a slow jazzy song with some creepy electronic noises. The lyrics imply that the titular "replicant" has killed his human counterpart.
Replicant why do you lie on the ground, Shoveling handfuls of dirt on yourself?
The creepiness factor doubles when Linnell begins addressing the replicant like a son. And at the same time, it becomes clear that something very wrong is going on.
Replicant, someone is waiting outside He says you did something wrong to his friend Look at me when I'm talking to you What have you got there behind your back? I found this when I was cleaning your room I think you've got some explaining to do Whatever you did, we'll get through this Go out the back and I'll deal with the cops
"The Darlings Of Lumberland". If the demented woodwind section doesn't at least disturb you, John Flansburgh's demonic altered voice certainly will.
The Dial-A-Song version of "Token Back To Brooklyn," which starts off with pitched-down voices repeating "get away," then kicks into a bleak, slow rhythm. To say nothing of one of the original lines:
The fare collector's drinking lighter fluid and claims he's killed our parents
"Stomp Box" is a fairly dark song, from lyrics like "Little stomp box tear it from my heart" to John screaming "KILL KILL KILL KILL KILL ME NOW..."
"I'll Sink Manhattan," a harrowing, emotional ode to hitting the Despair Event Horizon, backed by an instrumental that veers full-tilt between the ominous and the operatic.
"Aaa," off "Glean" speeds through lines concerning everything from tinfoil-hat conspiracies and impending misfortune to distrust of surroundings and grievous bodily harm.
What's this button do? I wonder what's inside this ticking Package that's addressed to me, and how are sausages made And what am I made of? I'm gonna find out now
The early and obscure Dial-A-Song track, "Hi Honey I'm Home". Don't let the innocent-sounding title fool you. The song consists of Flansburgh depressingly singing "Hi, honey, I'm home" backed to a droning two-note synth loop and the sound of a car crashing.