This is a tough question as there are a number of different ways in which you can decide whether one service is better than the other.

I have managed to narrow down the number of services in contention to two. These are Sitemeter and Stat Counter.

Having past experience with both of these services has helped along the way.

I think that if you want a free counter with a load of information on the persons location then you should get Stat Counter.

If you want your website and the services website to be faster loading and more detailed computer specifications but less on location then you should opt for Sitemeter.

They are two very similar services with Stat Counter beating Sitemeter on professionalism. I say this because it shows a map of where your visitors come from and a graph of visitors, unique visitors and returning visitors which is updated daily to show you how many hits you are receiving. Stat Counter has a log size of 500 entries on the free version so you can only look at the past 500 visitors detailed profiles.

Sitemeter is an easier service to use, the website is fast loading and it is far easier to navigate around.

My overall conclusion is that Sitemeter is the best free hit counter, even though, Stat Counter is better in other aspects of recording your visitor number.