Started with Webalizer, switched to Google Analytics.

Webalizer's ok, but it's missing a bunch of features like sane user agent string parsing (to give an overview of the browsers accessing your site). It also displays most of the stats by page hits (such as country and user agent) rather than "visits" or unique IPs, which I think is a better way to group.

I've been pretty happy with Google Analytics so far - it has a ton of options for sorting and grouping data (like viewing users' paths through the links on the site) and good IP geolocation. Plus, the JavaScript tracker gives you stats on visitors' screen resolution, which can be handy. On the downside, all our data is belong to Google.