One of the coolest and most helpful items you can add to a wave in Google Wave are the gadgets (click here for the google gadgets tutorial). When you start google wave you have 2 gadgets as a standard.
One standard gadget is the google maps gadget where you can pin point locations as a map that zoom right down to a street level. The maps sit within the wave without having to embed code or send someone out on an external link
The second standard gadget is a 'yes/no/maybe' voting gadget that places people at their desired answer when they vote. A great wee tool in a group discussion to get a clear picture of people's choices!
There are lots of site's coming out with links to gadgets that are being created by people. One of the best and simplest lists to navigate that I have found so far is here at Chaaps.com. It's an easy list to get through and has a range of fun and handy gadgets from the sudojku gadget through to the Ratings gadget.
The gadget function is not all fun and games. In a group setting when you are organising events gadget's such as the 'yes/no/maybe' do away with a lot of the backwards and forwards emails when planning and organising. Your map goes out to everybody and any changes can be seen by all and are noted as soon as you log in to google wave.
This would be a great way to collaboratively work within a team or for students to work when planning inquiries or investigating. It allows you to track who has posted work/comments but also easily allows for clippings, links, images, video and more to be linked or embedded within the wave giving you a complete overview of the journey in the inquiry process.