AVOID: paying for Amazon purchases directly with Citi Thank You points
Michael in the comments called Citi's Thank You Rewards earlier today, and was told that as of last week, Thank You Rewards no longer allows you to convert Thank You Points into Amazon.com gift cards over the phone. Citi has various variations of their Thank You rewards program (on various credit cards and checking accounts), so I don't know if this applies to all Thank You accounts or only some of them.
Executive Summary: Buy the $25/$50/$100 Amazon electronic gift cards through the Citibank Thank You program. Do not use the Amazon Shop with Points link for Citi Thank You because your buying power is only 80% there... Details after the break...
Some Citibank credit cards and bank accounts come with the Thank You Rewards program. The Rewards program already offered Amazon electronic gift cards in fixed amounts ($25, $50, $100). But what if you wanted to use your rewards for a specific purchase and pay exactly for the purchase without having a gift card balance? Recently the Citibank Thank You rewards program joined the Amazon Shop with Points feature. You go to your Amazon account page, look for the "Shop with Points" link and link your Thank You Rewards account through the participating credit/debit card to Amazon. This happens immediately if all is well, however, it is not a good deal! You only get 80 cents of Amazon buying power for every 100 Thank You points. Bad! You can verify this when your accounts are linked. You will see something like this: "10,000 points ($80.00)". Ideally, you want 10,000 points to get you $100.00 or more! (this is only an example; the numbers you see will obviously be different!).
Instead, if you redeem your Thank You Points by calling the Thank You Customer Service
at the Thank You website for an Amazon electronic gift card, you get $1 of Amazon buying power for every 100 Thank You points. And on rare occasions, Thank You may even have a discount on those gift cards, so you get $1 of Amazon buying power for 90 Thank You points. (UPDATE 3/19/13: you can no longer order Amazon electronic gift cards from the Thank You website but you can call the Thank You customer service and order them via a customer service representative at the same rate).
In general, when redeeming rewards from credit card programs, look for at least a 1:1 ratio between points and cents.