Firstly, before I answer the question in the title (as asked by a friend of mine scared of google), I think I am going to love buzz. It needs a few UI tweaks that allow you to follow people with loads of comments such as (I recommend) Robert Scoble, Jason Calacanis and Pete Cashmore, without them clogging up your screen but overall, it could be a twitter killer. I am not sure on the effect on Facebook as many many people using Facebook won’t have gmail, for example, the average non-geek user of Facebook in the UK will typically use their service providers email with outlook, they wouldn’t use gmail therefore would never hear about Buzz.
Buzz at the moment is restricted to three choices, use it, don’t use it and turn it off.
Before screaming and shouting, this is not a problem for your privacy, Buzz will only share what you tell it as a status update or what picture, video or links you drop in. It does not share anything automatically (unless you tell it to, such as twitter, blog feeds etc).
So to turn it off totally, as I just had to find out for a friend, is to simply scroll to the bottom of your inbox and click on “turn off buzz”. BTW, this is the official google line, so until they create a “delete buzz” button this is your only choice. Period.