Hello Frank,
Presuming you would want to do this through Moodle itself and not tinker around with the code, you could create a new custom user profile field and make it a required field.
If you would instead like to make use of the existing Moodle registration field. it would involve modifying 2 or 3 files (if memory serves). I will have a look around and post back if I do find something. I do recommend doing it through Moodle though because changing the code is a bit tiresome. Not only do you have to keep a note of the code changes, but you have to make sure that when you perform an upgrade you redo the changes again. And if the code changes (1.9->2.0 for e.g.) then you have to figure out where and what to change all over again.
Regards
Ravi