Trackers such as Google Analytics track the Traffic Source of your visitors. You can choose between Direct, Referrer URL and Search keyword when you submit your website.
If you want entirely anonymous traffic, choose the Direct Traffic Source. Google Analytics will show such hits as Direct hits.
If you want the traffic to come from a specific URL (e.g. http://twitter.com), choose the Referrer URL Traffic Source. Google Analytics will show such hits coming from the URL you specify.
For Organic Search traffic, choose the Search keyword Traffic Source.Back