Which web analytics tools do you recommend other than Google Analytics and why?

I really like Crazy Egg because the heatmaps there are of top quality.

statcounter has never failed me yet

AWStats i would recommend AWStats comes pre-installed by many web hosting companies.
Additionally, if you’re setting up your own servers, you can download it for your personal use.
AWStats goes deeper into the referring sites’ information than most analytics packages, and is a perfect tool for monitoring whether someone is hotlinking files from your site.
Besides being a great detective tool for bandwidth thieves, it offers all of the usual useful tools that you might expect from a statistics package.

since i am working at online radio station.
We use histats.com (it calculates the number of visitors and listeners to the radio) and before that i was working at a video game website and we were also using Histats for analytics.