One of my client's sites stopped tracking statistics with Google Analytics and I decided to look for alternatives. During my research I found that many people don't like hosting their visitors stats on external servers or waiting 24 hours to see them updated.

My first try has been Piwik, it runs on PHP 5, it's easy to install and uses Ajax for its widgets.

Piwik is open source and even if it's on a very early stage of development I suggest you to take a look.