I am logged into one web application all day long no matter what and that is Performancing Metrics. It is the easiest to use and most powerful analytics system for blogging that I have ever used. It is not a full blown analytics system, but it is everything I need for tracking my weblogs traffic. From its live spy feature that tracks users while they are on the site to detail IP data about users and an interface that accommodates multiple weblogs, it is well worth what I pay for a subscription. The beautiful thing about it though is that they have a free version so you can give it a run first without paying a dime. Go try it. You will be very glad you did.
Update: One really cool feature is the ability to assign a name or any moniker to an IP address. Certain companies visit my FaxChronicle.com website that are in that industry and I like to know how often they do. Again, this is a great product. I cannot recommend it enough. Try it out now.