I use Google Analytics, I find it to be more accurate than AWstats and the presentation of the information is much better. AWstats always seems to over count traffic. I don't know whether it is due to how it tracks visitors or less accurate filtering out of bot traffic but I never feel confidence in the numbers it comes up with.
If you use Adwords then Google Analytics is particularly useful as all of your campaign information is linked in with analytics. The e-commerce tracking is meant to be very good as well although it can be difficult to get it working properly with some e-commerce systems. If you manage it though it is invaluable to be able to have a precise conversion rate and value for different traffic sources.
I have just started using yoursitestats.com. It provides much of the info you'd get from other stats systems, but what's interesting about this one is that it's supposed to give users' other interests related to their lifestyles like their hobbies to help you understand your users more.