Amazon's customer service number is: 1-800-201-7575.
I found it in this article: http://www.slate.com/id/2091623/ and trust me please when I say that I had a lot less trouble finding their article than they did in finding the number.
And for those of you who want more info, I ordered from Amazon.com last week. An item costing $35.64. Imagine my suprise when I looked at my account last night and there were two identical charges in my account placed four days apart. Also, one of them was dated for April 9th... which hasn't actually happened yet. Amazon, when I reached them via their 'we'll call you' system, insisted they'd only put through one charge for one order, but promised it would be fixed by morning. Cue me checking my account to find the two charges still there at noon today. I had checked twice previously, but figured I'd give them a little bit of time to get to it.
Three reps later, they are still insisting there is only one charge and that they can put in a request for a reversal, but that it will take a week, so I call my bank. My financial institution of choice (USAA, which rocks the worlds of insurance and banking with their rocking coolness and awesome!) offers to place a three-way call to Amazon's customer service with me on the line so that we can resolve the matter.
Cue the hunt. I told the wonderful woman at USAA that I needed to do some research online in order to find the number first, and she agreed to call me back in 15 minutes. A thorough search of the site produced nothing, so I turned to a Google search. Immediately, I saw a flood of articles about Amazon.com's hidden customer service number. The Slate article was the first I clicked on. In the article, they make sure to mention the number three times, and their frustration is obvious as you read.
So, just to bring the total up to five, Amazon.com's direct, toll-free customer service number is: 1-800-201-7575.