I'm sorry if you were offended is the classic example of a bad apology. It can be used to sound as if you care, while avoiding any responsibility for the hurt that you caused.
Wikipedia's entry on Non-apology apology says:
- A non-apology apology is a statement in the form of an apology that is nothing of the sort, a common gambit in politics and public relations. It most commonly entails the speaker saying that he or she is sorry not for a behavior, statement or misdeed, but rather is sorry only because a person who has been aggrieved is requesting the apology, expressing a grievance, or is threatening some form of retribution or retaliation.
- An example of a non-apology apology would be to say "I'm sorry if you were offended by my remarks" to someone who has been offended by a statement. This apology does not admit that there was anything wrong with the remarks made, and, additionally, it subtly insinuates that the person taking offense was excessively thin-skinned or irrational in taking offense at the remarks in the first place.