In January Amazon expanded their electronics trade-in program with a $20 bonus credit for old Kindles. That bonus was set to end on 31 March (today), but earlier today I learned that Amazon is extending the credit indefinitely.
Simply fill out the appropriate form, send in your Kindle, and Amazon will credit you with a gift card on your Amazon account, and they'll also give you a $20 credit which can be used towards the purchase of your next Kindle. (It's a pity you can't apply the credit to the Kindle you purchased last week.)
They're not paying much for the oldest Kindle ($5, plus the bonus), but if you have a really old or non-working Kindle, or one with a broken screen, then this might be a better deal than recycling it or selling it on Ebay. But if you have a relatively recent Kindle in good working order and decent cosmetic condition, you could be better off selling it online. A 3-year-old Kindle Keyboard, for example, will only net you $20 from Amazon (plus the $20 bonus), but they're going for $30 to $60 on Ebay.
It's worth checking all of your options, and you certainly have the time to do so. Amazon's bonus offer runs through the end of this year, and the $20 bonus credit has to be used by the end of February 2017.
image by toejamnotearl