I remember the day in which Usenet was relatively anonymous. I could go off on how horrible someone was for liking blue shoes one day and come back a few weeks later and blast someone because they didn't like blue shoes. It was awesome. Unfortunately, when Google Groups came along, all of those stupid posts made in my youth were suddenly all brought back to life and, worse, anyone with an internet connection could search through them. This article describes how to get Google to remove those posts that you made and how to prevent Google from archiving them in the future.
To get Google to remove your posts, simply follow the instructions here:
http://www.google.com/googlegroups/help.html#9
To prevent Google from archiving your messages in the future, just add: 'X-No-Archive: yes' as the first line of your post. Some news readers provide this as an option, but, as far as I can tell, Google Groups does not.