I've had my Google wave account for several weeks now, but I've only used it regularly for the first week.
The google provided front end is a pretty ambitious web application that merges instant messaging, e-mail, and collaborative documentation (aka wiki) and discussion. Extensions allow for all sorts of other forms of collaboration - video conferencing, voting/polls, turn-based games, etc. Wave uses standard protocols on the backend (extensions to XMPP/Jabber) that will allow "federation" or organization-hosted wave servers that interconnect with others - similar to how organizations host e-mail and web servers today. To date, my experience is with the Google provided front-end and here are my impressions: