Every time somebody requests a item from our webserver it inserts a litle info about itself into the response header

Server:Microsoft-IIS/6.0

I've been wondering how to remove this since I think it pretty pointless

You need to create a httpmodule, 

public class WebsiteDomainModule : IHttpModule {
    // IHttpModule members
    public void Init(HttpApplication httpApp) {
        httpApp.PreSendRequestHeaders += new EventHandler(this.OnPreSendRequestHeaders); 
    }

    public void Dispose() {
        // Usually, nothing has to happen here...
    }
    public void OnPreSendRequestHeaders(object sender, EventArgs e) {
        HttpContext.Current.Response.Headers.Remove("Server");
    }
}

Just add a reference into you web.config file and that line is gone.

By removing that line we save about 25 MB of traffic data every day, about 3GB a month. Not bad.