I have used Webalizer, AWstat, Statcounter and Google Analytics.
Statcounter's feature where you can "cookie" yourself to exclude hits by yourself is nice. They are also one of the few "free counters" that don't require you to put their graphics on their site.
Webalizer and AWstat works in a different way than Statcounter and G.A., in that it analyzes Apache's log files. This means it can count all hits, also those that don't support javascript (ie. robots/spiders), but mostly you'll be interested in how many real readers you have. Using javascript and cookies also provides a much more reliable way of counting returning visitors.
If you can choose between Webalizer and AWstat I'd prefer AWstats, it looks better and has more features.
However, the king of web statistics is definitely Google Analytics (formerly Urchin). It has a ton of features, tailored for different roles ("webmaster", "marketing" et.c.), supports plenty of languages and different graphs. It recently also increased allowed sites from 10 to 50!
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