After my recent break-up with Google, I've had some adjusting to do. I'm taking it one service at a time.
I don't pay a lot of attention to the analytics for this site, but I do check about once a month out of curiosity and/or ego. I don't know what to do with the information but it is interesting to see the ebb and flow of article popularity. As of last week, I've moved to Shaun Innman's Mint analytics service. It's a one time $30 fee and all of the data is maintained on my own site. I lost all of the historic data, but it's virtually meaningless to me.
It was easy to configure for WordPress and provides more than enough information. I still have no idea what to make out of the information but it's still interesting. And I get to cross off one more Google dependency.