Please don't list this on a work's page as a trope. Examples can go on the work's YMMV tab.
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.
"The Darlings Of Lumberland" off Nanobots. 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 & 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 to the operatic.