Statistics: how important are they to you?

I’m just curious how important having access to a counter and/or statistics is to you. I have been through several different statistics programs, and finally settled on BBClone:
http://bbclone.de/
Check out their demo to see how it works.
Why? Well, for one thing, it fascinates me to see where people are hitting my sites from. Secondly, once I get my act together, I want to get the word out about my public health site and try to attract users from public health schools around the world. BBClone has a DNS resolving feature built into it that will return to me the domain name of most visitors. (I currently have this turned off, due to a performance drag.)
There’s a local file that installs with the software that references IP addresses to countries, so it’s fun, to me, to see the country flags.
I don’t have a visual counter displayed on any of my pages, because my opinion is that they can do two different things: wow people by showing them there are a ton of hits, or prompt them to leave more quickly because of low traffic.
BBClone doesn’t use a database, which is a little unique.
Overall, I’m a numbers kind of guy, and I like to look at the data, so it’s 75% self-serving. The other 25% is site-serving. Do you use a counter or statistics program? Which one? Why? How often do you look at the numbers?