Hey lhp,OK
1. You are not looking for a counter, your are looking for something that reads your logs files and analyses them 
2. The keyword u did not mention but implied is "free". I am not aware of any great log file analyzers which are also free.
I personally use WebTrends to track site statistics and have found it to be extremely accurate and highly cutumizable.
I suggest you try using www.register-it.com they have a "counter" which lets you track what SE is sending u traffic. I also suggest using the clear one, since it is my personal belief that counters are tacky, inaccurate and unprofessional. 
I've also heard of stats4all.com but I've never used it.
I hope this helps some... and if not others will probably know more about finding a service that will fit your needs