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Piwik [1] is a great alternative to Google Analytics. It is free, open source software, and it is typically self-hosted.

While I do not think it supports Do-Not-Track at this time, Piwik does have configuration options to respect emerging laws on data protection and user privacy.

[1] http://piwik.org/blog/2011/03/piwik-can-be-used-in-complianc...

> I feel it's impolite to subject your users to be tracked by Google and other huge companies just because they visited your website.

It's also probably illegal in Europe now, though at least in the UK the authorities have declared a one year moratorium on taking action over it because the new privacy rules on cookies etc. are practically unworkable even if well-intentioned.

Analytics software on your server has the advantage of tracking images, css, js, and other non-html-page files, and still works when your users use addons like Noscript, Adblock, or Ghostery.