Using Tomcat, how can I log each and every call to the servlet engine (something like apache-access.log) ?

As of version 3.2, the standalone version of Tomcat does not provide an access log. It depends on the containing web server (e.g. Apache) for that function.

If you feel like it, it would be straightforward to write an Interceptor that does this. Subscribe to tomcat-dev@jakarta.apache.org, check out the latest CVS tree, and have fun! That's the beauty of open source. (Make sure you support the W3C standard log format, and see the Catalina source for inspiration; there's code in there for formatting access log entries.)