Right now i use statcounter.com and I really like it. The major limiting factor is that it has a log of only 500. I go through that so quickly it isn't worth it and doesn't give me all the info I want. Do you know any free counters that are invisible, track unique hits, no log (or more than 500)?
Why do you use any of these things? All the stats you need are in your control panel. These are mostly just malware loading devices.
Doesn't your host provider have a free counter? I use Network Solutions and they come with a free invisible tracker which tracks visitors by unique visits, IP, etc. They do have their limits and that's where you can use Google Analytics to complement it.