I the worst headphones I have heard for the money were also the worst headphones, by far, that I have every listened too.......and by some horrible twist of fate I had them twice.
They were some large black sony circumaural cans, $49, I cannot remember the name as this was about 10 years ago, they looked kinda like
these (but those are not the same model)
At the time I was in Jr. high and listening too music out of a crappy little $80 boom box. I plugged these and my music sounded awful, especially NIN(one of my favorite bands at the time) There were no details to the music at all, whole sections of music were missing even if you turned the music up to 11.
There was so much bass in them that even when EQed all the way down it was still present, and no amount of EQ would bring back the missing detail. I scraped together some money and got a replacement less than a week later.
Fast forward like 3 years later, I was 15 or so at the time, my dad had accidently broke my headphones, and the next day when he got home from work he handed me the replacements he bought me..........those same sonys. I kept telling myself "no they just look similar" plugged them into my computer and ohhhhhh god no! It is the same ones, no details in the music at all, what a bad twist of fate.
I don't think I will ever find headphones that bad again, the $7 clip ons I use now for the gym sound better.