You can go to your trash and click 'delete forever' to stop the messages from being stored. After 30 days your messages will not appear in the trash to 'delete forever' though and they will be stored by google indefinately.
I have google wave, but I guess I'm not that popular. I only have 2 people on my contact list. Maybe when I get into a classroom I'll make more use of it.
I've got google wave, but I'm not really sure what to do with it. My brother did put a sudoku game in one of our conversations, and I've got it connected to twitter somehow.