Wave is a tool, and like any other tool, can be put to a lot of different uses. Here is my list of uses that wave is currently being put to, and that I think it will be used for.

1. Email Replacement Google initially marketed Wave as a replacement/update for email. While it does have the potential to do that, since its structure seems much closer to the way people really communicate than email, I think that email is still way to popular to ever be replaced completely. When at some point it actually goes into open Beta, I will encourage all my contacts to switch to using it. How many of them will actually make the switch only time will tell.
2. IM Replacement Similar to the email replacement idea, Wave would work great as a replacement for IM, since its realtime nature is ideally suited to Instant Messaging style communication, and the fact that the conversation is stored means that it is a lot easier to find the conversation later (While a lot of current IM implementations have the ability to log a conversation, I find the implementation counter-intuitive). The real time typing actually makes the IM experience closer to areal conversation, as I sometimes find myself framing the response before the person I am talking to has finished typing (not necessarily always a good thing, though)
3. Note-taking Wave can be used as a good note taking tool, either for brainstorming (possibly with a mindmapping widget), or just take notes during a meeting, lecture or presentation. This could be done in a private wave, or possibly with several participants, working together, making sure that all the relevant information gets recorded.
4. Scientific Collaboration I really think that one of the areas where we will see Wave shine is for scientific collaboration. Modern research papers often have dozens of contributors, and using wave would enable them to exchange information and work on papers together, as well as comparing notes and theories. There is already an extension for chemical visualization developed for wave, and I am sure many more to come.
5. LiveBlogging Really a variation on note taking above, but in this case the focus is on producing the record of an event as it happens, in order to provide an audience with an impression of what is going on, rather than notes for later review. All the points that I made about taking notes above apply here. The structure of the wave would allow participants that are not physically at the event to ask questions and demand clarifications of the people that are.
6. Games Having written about Gaming and Google Wave already, there is not much to add about this one.
7. Collaborative fictionAuthors (and possibly fans) could collaborate on works of fiction, using wave to discuss characters, settings and plot, and then creating a separate wave in which they can work together to write.

Of course, there are many more potential uses for wave (there were at least 52 listed on the wave dedicated to that topic, and the list is growing steadily), but these 7 are the ones that I think we will see the most growth in.

What do you think, what kind of uses can we expect to see from wave? (and what kind of uses have you already seen?)

Related posts:

1. GTD and Google Wave
2. Google Wave Searches
3. The Death of Instant Messaging