Amazon has unleashed their private app store for Android phones which competes with Google's own Android Market store. It looks promising, with all of Amazon's ratings and feedback and pricing smarts, but underpopulated on Day 1 - no surprise.
On the phone side, installing the Amazon app store requires allowing the installation of apps outside of the Google Market, thus requiring a visit to settings, applications to check a box called "Unknown sources." I had no problems installing on my Nexus S with T-Mobile though AT&T customers are at least initially locked out because AT&T doesn't allow so-called side-loading of apps.
There are a bunch of apps but not many thousands. At least right now, if you buy an app on the web site, you still have to open the Amazon app store app on your phone to install. Apps you buy in the web version of Google's Market just install themselves automagically.
There is what should be a pretty cool feature allowing you to "test drive" most apps in your computer's browser in a virtual Android phone. But I couldn't get the test drive to work on my Windows computer and the button doesn't even appear on my Mac. Hmm.