Farhad Manjoo has a post over at Slate explaining why this is the case. It's nothing new, but Manjoo does what he does best, which is aggregate all the information into one, easy-to-consume article:
Why doesn't Amazon charge you sales tax? It has to do with the regulations states use to determine which companies must collect taxes. According to Quill Corp. v. North Dakota, a 1992 Supreme Court ruling, companies are only required to collect sales taxes from their customers when they have a presence in the state in which they reside. If you buy something from the Web site of a company that has physical stores nearby, you'll most likely have to pay taxes. When you shop at online-only stores, you pay tax only if the store has substantial operations in your state. Since Amazon's headquarters are in Seattle, you have to pay taxes if you live in Washington State, and because it has warehouses or other facilities in Kentucky, Kansas, and North Dakota, you've got to pay taxes there, too.