zumotemo: Pretty much what the others said about giving them a safe storage area that keeps the dust and moisture out.
I live in the desert and dust is a very real part of life here. I store any unused devices in zip lock bags for dust prevention. Those devices connected to my computer get cleaned of dust accumulation (including blowing out the interior of the computers) at least once per week. Headphones, (and boom mikes) cameras, monitors, etc. get cleaned (while turned off) with proper cleaners designed for electrical equipment and thoroughly dried before being powered up. I keep my connected headset in a large plastic bag when I'm not wearing it (still connected to the computer, but the bag zipped to only allow the headset cord to pass through) and even my desk camera has a plastic dust cover over it when not being used.
I have some friends who live in very humid climates and they go as far as putting the packs of moisture absorbent material (silica) that comes packed in electronic equipment inside the bottoms of their computers. If a computer is used daily, the internal heat generated is normally sufficient to evaporate any moisture, but if one is stored for any length of time, moisture can build and when powered on, destroy delicate circuits.
what to do with not in use headphones is to deposit them in a place where dust cant settle on them, because that is to nasty to have dusty dirty headphones when time comes to use them. the closet for example would be a good dust protected place to deposit not used headphones.
all depends on the make and model of them and how much you paid for them and if there super expensive put them somewhere where there not gonna end up getting destroyed
Throw them in the trash
store them somewhere safe so they don't get destroyed.