2013 entry: you can only apply to one course at either the University of Oxford or the University of Cambridge. The exception to this has changed: if you will be a graduate at the start of the course and you're applying for graduate medicine (course code A101) at the University of Cambridge, you can also apply to medicine (course code A100) at Cambridge, in addition to being able to apply to graduate medicine (course code A101) at the University of Oxford. No other combinations are permitted.
Don't forget that the deadline to apply to either university is 15 October and you may be required to complete an additional application form from the university. Further information is available on the choices page.