The nice thing about email and IM is that they're very KISS, message goes from client - server (sometimes) - other client. Wave was built with the Google mindset of server-server with web-only clients. Sure, there was the CLI app, but it was more of a proof-of-concept than Outlook or even Mail.app for IMAP.
In terms of a project, Wave would greatly reduce the overhead of emailing in my project teams. We do web development, and there's a designer, PM, writer, AM, outsourced QA, and me, the developer. Right now there's this huge, hulking in-house business tracker meant to coordinate between the parties. Using a wave per site would be great, as we could all communicate on the same whiteboard.
If you're still doing real-time collaborative, SubEthaEdit or ZoHo notes could fill the gap. Or, you could host the server yourself?
I think this is already the case. Didn't Google demo a command-line Wave app?
We still use Wave for collaborative document editing at our startup, although we clearly need to migrate off ASAP. :-) Wave seems to work best as a small group collaboration tool. It's not so useful for communicating with strangers, or for real-time chatting (the key bindings and performance aren't well-suited to short, real-time messages).
Wave is a great replacement for short-lived wiki pages. You know all those wiki pages that you work on intensely for a while, and which then hang around cluttering up your wiki? Wave is infinitely nicer for that kind of emphemeral, searchable documentation. And you don't have to teach non-techies how to use MediaWiki, which is always a plus in my book.
Oh, and install a Wave notification plugin in your browser. I use "One Number" for Google Chrome, which supports Gmail, Wave, Google Voice and Google Reader.