That's called your access log. I haven't seen a hosting account yet that didn't have an access log available somewhere. Just download the log every so often, run a short script on it to analyze whatever, and put the results back on the server. You could even automate the process with Net::FTP.

You could also run your log parser on the server, but I wouldn't personally recommend this if it's programmed in Perl and the log is large. It'll eat up too much resources and irritate your hoster.