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Have a look at Google Analytics. You have to signup with them and then put some code on each of your web pages. This method can not go back in time to give you previous stats. On the plus side you don't need access to the server log files. It also has a bunch of features like a map indicating where traffic is coming from.
Another option is to run a program on the web server log files. A couple you can use are webalizer or awstats. This method can go back as far as the log files go back. To use it you need to install some software (it doesn't need to be installed on the web server but you need the log files).