Amazon isn't just a juggernaut when it comes to buying things, it's a great place to sell them as well. Part of what makes Amazon such an attractive place to sell your stuff is that your used stuff goes right up for sale next to the new versions of the same products—so anyone shopping for, say, a Nintendo 3DS, will see your offer under "New and Used" right next to the price for the same item new. If they're interested in saving a few bucks, it's one click before they see the one you have for sale—and considering how many people browse Amazon for just about anything, that's a huge potential audience.
Plus, listing your item is super easy, even if you don't sign up for Amazon's fulfillment program. You list it, wait for it to sell, then ship. If you really want, you can send all your junk to Amazon, let them list it for you, then handle the shipping and customer service after it sells.
All that said, Amazon isn't a panacea, and just as many of you called that out in the nominations thread as people who praised it for its ease and fast selling. For one, if your item sits in Amazon's warehouses too long, you'll pay fees on it. Amazon also takes a big chunk out of your sale price, and other prices severely limit how much you can make on your used stuff.
Plus, Amazon's shipping credits are never enough to really ship an item, so you wind up losing some money either way. Still, others of you highlighted Amazon's direct buy-back program, where they'll just buy your stuff from you straight away, and their free shipping in their fulfillment program—so you can send your used stuff to sell free of charge.