I have used it extensively with a geographically disperse group of friends and I, at least, will be sad to see it go. It was superior to IM, IRC, etc., in one single respect:
It allowed for full-historied asynchronous conversations.
The core functionality was akin to IM, but with the capability to drop in and out at will. We would take turns starting the Wave of the day and encapsulate a rolling "conversation" each day, with folks contributing jokes, interesting links, YouTube videos, etc., at their leisure, and (here's the best part) everyone could get caught up immediately simply by reading through the history.
I would not have connected with these friends in the same way had we simply had a group IM room, or an IRC channel, or a forum. Forum posts feel too "heavy" for the transient nature of many of the observations we had, while IMs are too easy to misplace and take out of chronological order. Wave's threading alleviated the latter and the former.
What really made it hard, though, was the lack of a coherent export process. There were some Waves we wanted to save for posterity's sake but, until very recently, it's been a nightmare to get the data out.
*shrug* I know it wasn't for everyone, but my friends and I will surely miss it.