I'm looking to switch from Nedstat Basic (a free, decent web stats service but forces u to put a button on your site and makes your stats public) I realized having public stats is probably not a good idea.
There are plenty of free and cheap perl scripts available at Hot Scripts [hotscripts.com] or if you have access to your raw log files you may like to try Analog [analog.cx] or the one I prefer LogFile Analyse [jan-winkler.de] ..both free.
I agree with shelleycat that it is not as good as direct access to logs, but I do not have such access (you gets what you pays for).
The Hotscripts category you want would probably not be the one linked above, but this one: Remotely Hosted/Web Traffic Analysis [hotscripts.com]. The other ones are scripts to install on your own server and as such not really comparable to Nedstat & Co.