On-campus interviews are not required. In fact, there are a great deal of schools that do not offer them. Even those that do have on-campus interviews often do not have them year-round. In general, schools will contact you for alumni interviews in your area. Below is a list of some schools, broken down by whether or not they offer on-campus interviews:

YES: Harvard (offered from September to November), Yale (offered from mid-June to mid-August and mid-September to mid-November. Note: Yale cannot accommodate all requests for on-campus interviews)
NO: Princeton, Columbia, University of Pennsylvania, Cornell, Brown, Dartmouth, Stanford