An 'offensive' music video changes depending on many features such as where in the world it is based and what time era it has come from. This makes the definition of offensive very hard to define, many music videos have been banned for a multitude of different reasons.
The first music video ever to be banned was 'Girls on Film' in 1981 on MTV, this was because it was said to expose too much flesh.
An artist who had a lot of her videos banned was Madonna, particularly 'Justify my love' because it seemed to involve excessive amounts of Homosexuality, sadomasochism and group sex.
Music videos have been banned for all sorts of reasons such as religion, nudity, violence and drugs, even seemingly innocent music videos have been banned so as to make sure that absolutely nobody could be offended by it.