The Amazon App Store for Android is open for business, at least for now. Apple is objecting to Amazon's use of the name "App Store," and is suing to make them stop.
The suit claims that “Amazon has begun improperly using Apple’s App Store mark in connection with Amazon’s mobile software developer program.... Customers of mobile software downloads are likely to be confused as to whether Amazon’s mobile software download service is sponsored or approved by Apple.”
On the other hand, Angry Birds Rio for Android is free for a limited time! (Perhaps more limited than Amazon realizes.)