The most obvious alternative is probably Piwik[1], which offers similar basic functionality to regular Google Analytics out of the box, but is also Open Source and highly customisable/extensible via a plugin model.
Among the features threeseed mentioned, funnel visualisation is probably the weakest area in the baseline version right now. There have been various plug-ins available to do it for a long time, but it's not built-in yet. That said, this area is underpowered in GA as well, and at least with Piwik you can do something about it (and people actually do).
Piwik has been in development for nearly a decade, has been downloaded millions of times, and is in active use by high-profile, high-volume sites. It's every bit as production-ready as Google Analytics.
[1] http://piwik.org/