I have been using Google Analytics for quite some now and have been really pleased with all the stats the service offers. The only thing missing has been real time stats. Woopra gives you that in a desktop client that looks fantastic and offers users a ton of information.
Here are some of the stats you can view in real time: IP addresses, geographic locations, user browsing data, visitor history, visitor paths, arrival and departure points, country, operating system, browser, language, screen resolution, pages viewed and time spent on pages. All of theses stats are searchable. You can even "live chat" with users.
Woopra is still in beta but it doesn't take more than a couple of days to get your website approved. To get started, register at Woopra, submit the url of your website and in a couple of days you should be approved. Once approved, you can insert a piece of code into your template (or there is a plugin for Wordpress sites), download the application (Mac or PC) and you are all set.
The free service is limited to websites with less than 10,000 page views per day and you must have the latest version of Java enabled.
If you have your own blog and this interests you, give it a try, I think you will be pleased.