With ad blockers, user tracking gets harder and harder, and this sucks when you want to understand the effects of changes on your own website, such as changing user menus, moving content blocks from a position to another, or even to a different page, etc. The value of partnerships with other websites gets harder to evaluate too.
Hosting my websites on Linux environments, I never stopped using server-side generated statistics (based on Apache's access logs) with tools like AWStats. Used together, I feel that client and server-side stats give a much better image of what really happens on my websites.
But in the end, I feel awstats isn't enough, and I'll take a look at other solutions that have been pointed out in these comments. Thanks!