9
You can use the noscript and ghostery addons in Firefox to see when your browser is attempting various api calls to Google, Yahoo and others. When you are in a regististration page that uses apis.google.com or recaptcha.googe or whatever these will tell you that there is a third party dependency.
Using the standard n + n captcha in XOOPS 2.5.6 standard profile, there are no observable dependencies, however several versions of profile modules have made use of Google recaptcha, Wishcraft seems to love those third party dependencies for some reason. I believe as Mamba says you can configure to third party recaptcha if you want to.
PIWIC is a good independent analytcs script for local use that uses a JS tag, much like Google Analytics does. Downside is that if uses disable their JS, you go dark on their visit.
AWSTATS or WEBALIZER use server log and provides general stats, but do not provide user level tracking analytics.
None of these phone home to the Google/Yahoo/MS big brother ratpack.
XOOPS also has TDMStats and irmtfans User Log modules, but I have flagged what looked like XSS errors from the former.
