AWStats is also nice, but it doesn't make use of much of the context available to a Rails app. It also doesn't have quite as much information as Analytics.
There seem to be any number of plugins available, but none of them seem to stand out above the others.
What do you guys use, if anything?
So far I've found the best solution is to build whatever important trends you want to track (ie. which readers have viewed what article) as part of your app, include Analytics anyway (it's no effort at all to add), and for any serious number crunching take a snapshot of your database to do some calculations from (off server).
Really though, if someone has a good Rails solution, they should build a plugin :)
Unfortunately doing the analysis of the production logs daily doesn't work as it takes hours to analyze my logs (I get 400k page views not including robots a day), so I run log_rotate/pl_analyze every hour.
Each hour I get a report that looks like http://pastie.textmate.org/private/dwig0jfl5osjqq1hqoeakg
That said this isn't enough and I have ideas of how I want to fix it, but I've not had the time to implement them.
Also talk with EngineYard - they are in SOMA, and are involved in the ruby community. If Ezra and his team don't know how to fix it they will know who you should talk to.
disclaimer I am an EngineYard customer
We've been using it with http://dancejam.com and we are very happy. New Relic has a great product. I wish I had an account for userscripts.org as well :)
One app we're currently trialing with scout (scoutapp.com).. looks promising so far, I haven't had a chance to go in and really look at the data produced to far though.
Also their beta has event tracking that is usable from both flash & javascript - and is very useful