Due to the privacy flaw in Google Buzz many users have decided to stay away from Google Buzz updates. I am also not much impressed with this new service so i have simply turned this feature off for now in my Gmail. If you are also looking to get rid of Google Buzz in your Gmail account then here are the two ways you can follow to keep it away from your Gmail.
1: Disable [Turn Off] Google Buzz completely:Doing this will completely switch off the Buzz service in Gmail but can enable it future whenever you want. To do this simply click on the “Turn off Buzz” link in Gmail footer portion. See the screenshot below to locate that link.
To enable the buzz in Gmail once you have disabled it, click on “Turn on Buzz”. You will find this link exactly at the same location in Gmail footer where you got the “Turn off Buzz” link.
2: Filter/Remove Google Buzz updates in Gmail: If you want to ignore/skip the updates from Google Buzz then Adam pash of lifehacker has a simple solution for this. Headover to this link for guide on how to filter the Buzz updates in Gmail.