Oh gosh. How much google analytics did I put during the 6 months where I thought it was the alternative to parsing logs for stats on my server when I believed in the clown and migrated to it?
PS: I try to quit looking at stats as much as I try to quit smoking ; it is the only sensible alternative. I should not care about them.
Piwik is excellent and simple, and SnowPlow is very powerful if not user-friendly.
Server logs are pretty unreliable, and don't give nearly the depth of data that a true analytics service does. I think a self-hosted analytics service does very little harm, as the main danger with Google Analytics is the potential for cross-domain tracking.
Officials can then claim with a straight face that it is only meta-data - they only need to log the request with all the data in it, not the response from the server, which is usually a transparent 43 byte GIF.
By using your own server, and modifying the default URL structure, a government has to track your site directly, which is unlikely unless your site warrants interest. And if everyone did this and had HTTPS, the NSA's job goes from cracking a handful of provider's HTTPS (Google, Adobe, etc) into cracking hundreds of thousands.
The argument is that it's trivial for sites to share and network their results, building up a profile and effectively tracking users across sites. It completely sucks because 99.99% of people with Piwik are not doing so, are not tracking, are not delivering spam, or ads and just want to know how people are using their site.
I care about stats as a junkie and I see this as vanity or OCD.
Best solution at my opinion is to not care and just practice.
For a simple site, weblogs probably give enough information to perform site optimization. I do think that there are lots of stats any website of sufficient scale needs to fine-tune operation/marketing which are NOT available via weblogs and in fact require some JS to be on the page.
There should be a way to get this limited information without infringing on privacy and without having data gaps from ad blockers.