First things first: unlike other audio components, you wear headphones. They're in intimate contact with your ears, hair and head. That might be a deal-breaker for some folks considering used headphones, and I understand.
Some will no doubt be put off by hygienic concerns, but others won't. Do you ever put on headphones in record stores or museums? I do, and hundreds, if not thousands of people before me wore those headphones, too.
It's worth pointing out that, with a lot of the better full-size headphones from AKG, Audeze, Audio Technica, Beyerdynamic, Grado, Hifiman, MrSpeakers, Sennheiser and so forth, the ear pads/cushions are user-replaceable, and a few offer user-replaceable headband padding. When in doubt, check with the manufacturer about a specific model.
Buying used doesn't make sense for cheap headphones, but if you can grab a used high-end headphone for a fraction of its original cost, that might be a good investment. As I looked around I noted the very best, most highly sought-after models aren't heavily discounted on the used market. That's an indication that the best stuff holds its value, but there are deals to be had. They're out there -- keep looking.
I bought a used pair of Sony MDR-SA5000 headphones a few years ago for $200. They were $700 when they were new, and they're still a terrific headphone. I doubt Sony offers service or parts for that 'phone, but some brands, such as Audeze, Grado, Klipsch and Koss for example, usually do. If you have concerns, try contacting the company and ask about their service policy; if they don't respond, better not take a chance on a pricey used headphone.
Some great sources for used high-end headphones (and headphone amplifiers) are eBay and also Head-Fi. Even better, I recommend Audiogon. With classified ads don't hesitate to offer less than the listed price. Of course, buying anything used is not without risk, and you really should check the seller's feedback prior to purchase. When in doubt, wait for something better.