Looking at this article on Slashdot led me to an open source version of Google Analytics namely Piwik.

Installation of Piwik is very easy and It has a WordPress Module, WP-Piwik so integration into a WP blog isn't too difficult. Another benefit is you get a stats page integrated into your WordPress Administration Area which saves having to log in to GA.

For high traffic sites it pays to run a cron job to automatically compile the stats every night.

I found the piwik archive.sh file located under ${piwik_web_root}/misc/cron/ required an edit because it searched for and couldn't find the php5 binary in $PATH on my Dreamhost webhosting account:

# comment this default out
# PHP_BIN=`which php5 2>/dev/null`

# hard code the path to the php5 binary
PHP_BIN=/usr/local/php5/bin/php