Tweetstalk allows you to follow Twitter users without showing up in their Follower's list. Currently you need to have an invitation code to sign up for their services. It is pretty easy to get the code, all you need to do is to follow @tweekstalk. You will then need to download the FireFox Add-on to get the "Stalk" button to show up on Twitter accounts.
There are many reasons why you would use an application like this. Maybe you want to monitor what your employees are saying on Twitter, stalk your ex-girlfriend or boyfriend to see what they are saying, or you want to follow one of the many job related Twitter accounts without your friends/colleagues knowing.