We have several stats packages available via the hosting provider, but I rarely look at them anymore. I do save all of the raw monthly log files here, which can be used to analyze things to death...
I also added Google Analytics to the site back in May, which provides many useful stats not available in log files. For example, it shows user screen resolutions (8.4% of our users are at 800x600, everyone else is 1024x768 or higher), connection speeds (5% of our users are still on dialup), average visit time (11 minutes, 15 seconds), and many other interesting tidbits. All of the data gathered is aggregated and anonymous - a good combination that allows privacy of users, while providing useful details to webmasters to improve site design and content.
Attached is a brief overview of our site stats, starting in 2004. Nice and steady growth...