1. Google Analytics is the most popular free analytics tool.
2. Chartbeat is a newer, interesting analytics tool that works in real-time.
3. Quantcast will let you show your traffic stats publicly and will tell you demographic information about your web visitors.
4. Mint is a gorgeous, real-time stats tool with lots of plugins available to add on new features.
5. Omniture is the big daddy of analytics software and will do almost anything you want, but it is very expensive.