Google Wave seems like a strange tool at first and has so many use cases it can seem overwhelming. One thing I use it for is as a wiki. To keep organized I first make a main wave that just has links other waves of the same topic. Google Wave makes it easy to just drag and drop links and files (though it’s a little buggy currently). Next I put whatever into the wave say a design specification. Under I can put blips (which are like reply’s in a forum) to discuss the document.
That said there are some shortcomings I hope will be fixed before Google takes it out of beta. I’d love to be able to export the wave blips to other sites. Say I have an official documentation site for some project that I want nice looking information. This information could be the design spec I mentioned but only the first blip so comments and changes could be made in Wave will a nice finished product always exists elsewhere. Currently it does integrate with blogspot, hopefully more will come and it can be used almost as a content management system, this would be really awesome.
Another problem I run into is knowing when a wave is updated. I solve this with firefox/chrome extensions but this isn’t ideal when trying to work with someone else who doesn’t have them and isn’t alerted to when the wave is updated.