Are there any free services that increment a simple hit counter without tracking the users of the site?

I would like to know how many visitors there are to my site, excluding bots. I don't need detailed information like unique visitors or where the user is from (in fact, that's exactly what I don't want). I have been researching free hit counters, and it seems that most (all?) of them display advertisements and their terms of service indicate that they can use the data they collect from the client site however they want. Google Analytics also does this and tracks users across sites.

The site is static HTML, so an external link or iframe of some sort is easiest for me to implement. I could switch to a Ruby or Node.js back-end, in which case lots of other options open up (like Ruby impressionist and more low-level implementations), but my hosting service is pretty limited.

If the answer to my question is simply "no," what are my other options?