I run Piwik on OpenShift to collect stats on visits to this blog. I'm not really interested in knowing who visits my site. I'm only interested in knowing what people are visiting for, and how: which pages are more viewed? where are people landing to my site from? how long after publishing some post do people still visit it? And so on.
One of the ways this is also helpful is to track 404 (page not found) errors that pop up for visitors. After migrating my previous posts from blogger, I kept monitoring for any posts that may have been missed by the automatic migration process, and manually moved them.
These days, the 404 tracking turns up interesting data, though. Someone recently tried to access such a page on this blog which resulted in a 404 error:
A quick search on the net revealed it's a relatively recent vulnerability discovered in some php-based e-commerce suite, which gives root access to the server hosting the software. Thankfully, I don't run any e-commerce software, and I also run on OpenShift, which gives the servers quite a bit of protection. In the worst case, some wordpress vulnerability might affect my blog, but the other software hosted on the same server as this blog will be protected (even in the case of a root expoit).