A little biased, because I try to hand-wash as much of my laundry as I can - and don't even own a machine dryer, but here goes.
I have an all-spandex binder, from underworks. This gets washed whenever it starts to get gross. This could be one full day, or as long as two weeks. I wash it by hand or in the washer, cold water, a bit of grated soap. If it's getting stained or discoloured, I make a paste out of water and washing soda + baking soda, and let it sit for a few hours before rinsing it out with vinegar and washing it. If it's still stained, I hang it out in the sun to dry (when available) by the bottom - never by the straps. Otherwise, it goes on the racks inside to dry. I wouldn't put it on a hanger even if I bothered to hang more than a few of my clothes.
Velcro-side binders, or with a front zipper (like from t-kingdom) I have a couple of. They get washed every 2 or 3 wears (more often if it's hot out and I'm sweating, or they start to stink or anything) with the rest of the clothes like usual, and hung out to dry with the rest of the laundry, wherever it ends up. I don't put these on hangers either, but I don't imagine they'd mind.