Whatcounter.com provides you a free invisible counter and statistics service. Paste some code on the pages to be tracked, upload a small .js file to your server to relay the info to Whatcounter.com and you're all set to get best info available:- visitors ip (proxy & real IP), full user agent, traceroute, search term used, top referrers,all referrers, visitor paths (which pages they visited), links to site, screen resolution, OS, browser, country, track file downloads, display users online, make counter visible if you want and lots lots more....
