To trade a game in to Amazon, all you have to do is visit the trade-in section of the site, select the games you want to trade in (at least $10 worth), print a free shipping label and send it out. You'll get a gift card in return -- plus an extra 10% if you do it before March 19. Unfortunately, the trade-in values seem roughly commensurate with GameStop's, which means they're pretty low. But sometimes eBay is such a hassle!
We wonder about GameStop's future if enough retailers band together to provide GameStop's services without requiring people to visit GameStop's stores.