In celebration of the Guardian's slot on unintentionally frightening songs, I'll go first:
I always found listening to Peter and the Wolf to be a bad experience, probably due to seeing a jerkily animated Russian version of it in the school cellar, which being Thatcher-era was where the TV was kept. That 'Do-do-doo, do DOO do-doo" bit always conjures up the menacing scene in which a horribly moulting wooden wolf jerkily circles a tree in which a wooden bird is hiding.
That "every time you go away, you take a piece of me with you' song used to give me the creeping horrors, largely due to my mishearing 'me' as 'meat.'
Puff the Magic Dragon is deeply wrong on so many levels (it still actually has the power to actually depress me for days after hearing it), as is Teddy Bears' Picnic. It's suspiciously perverted in tone, ("If you come down to the woods today, you're sure of a big surprise...!" and sounds even worse when heard as a kid in the local park as a part of the Morecambe illuminations in the inaccurately named Happy Mount Park
In a touchingly mistaken adult attempt to make it more 'fun' they'd hidden little speakers in the trees, so you'd get this disembodied teddybear song playing out of sync with those horrible budget animated bears (slowly moving their limbs up and down) as a centrepiece. Quite horrible. XD
"Seasons in the Sun" by Terry Jacks was the most awful, sickening lump of sentimentality I've ever heard. I did, and still do, find it physically sickening to listen to. It's that stupid "Goodbye my friend, it's hard to die..." Rather that being sincerely sad and affecting, it's actually quite repulsive, especially with his awful fucking voice. Anything by Chris de Burgh also has this effect. It's quite horrible that he was ever given life at all. Like those stupid films with some teminally ill love interest.
Existential despair songs are another goldmine. It's usually caused by the Beach Boys' 'Fun, fun, fun' They all sound so hysterically cheerful that it puts you in mind of the forced cheerfulness of a suicidal clown, and they seem to give you the feeling that the world is but a sad, searing Sunday wasteland.
As far as embarrasingly weird fears go, I was also scared of 'Mr Soft' by the Steve Miller Band, 'Waltz in Black' by the Stranglers, 'Waterloo Sunset' by the Kinks, 'Waltzing Matilda' the 'ghostbusters' theme, Elvis Costello as a person, The Carpenters (they gave me the creeps) and an entire Enya album. It scared the bejaysus out of me.
Oh yeah- and 'We Three Kings of Orient Are." It starts tamely enough, but for those that have endured learning the whole damn thing you realise the verse slows down to a leanden dirge, culminating in
"Myrrh is mine, its bitter perfume
Breathes of life of gathering gloom
Sorrowing, sighing, bleeding, dying
Sealed in the stone-cold tomb"
I can imagine a little Ian Curtis singing that in his school choir. O.o It had the most indelibly creepy effect on anybody who had to sing it.