[Helgen]

I forgot the term used for the type of headphones which let you use your own headphone jack cable in them. I saw some woman a while back with a pair, forgot the name, but she could take out the jack from the headphones (standard headphone jack.)
 
Some recommendations for some under $100 would be especially great, thanks!

 

[Hexidecimal]

You mean headphones with a detachable cable? The cable can be removed from the headphones themselves? If all you want is that, under 100 bucks I have the Shure SRH440s, which provide good sound and that functionality.