Got my invite for Google Wave a couple of weeks ago, and I've been playing with it a bit. Stable it is not. Bug free it is not. But fun? It could be. Useful? Maybe.
My first impression is that it is a bigger, better version of instant messaging. You can embed documents into a wave conversation. You have message history like email, but anyone can edit any of the messages in the wave, which could be bad. A tie-in with Google Docs would be great for shared editing of a document, but Wave doesn't have that yet.
Moving a wave to the trash is flaky, as is the indicator that you have unread messages. Signing off, killing the browser window, and signing back on helps. Wave is a long way from the polish that Mail and Docs have.
It could be useful if you have a spread out team of people or a lack of suitable conference rooms and you want everyone's opinion on a document or idea. You could write a round-robin story in a wave. You could arrange a group lunch, or have everyone watch The Muppets: Bohemian Rhapsody clip at the same time. Wave has definite applications, and drawbacks.
(I have a few invitations to give away, drop me a comment if you want one.)