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Email updates can be turned on via the Inbox dropdown menu. Once on, Google Wave will notify you with a summary of updates to your waves and email you when you're added to a new wave. Thankfully you'll only receive one update for each individual wave -- instead of receiving an email for each update to a wave -- until you log into that wave again.
As notifications are still in the testing phase you can definitely expect the experience to be somewhat buggy. Google warns that you could get notifications for updated waves even if you're the one that made the update, you can't turn off notifications via the email link, and information in the notification may not show all the participants in a wave.