The only correct actions are those that demand no explanation and no apology.

Has anyone ever apologized to you like this?  "I'm sorry if you were offended."
 
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.

What do you do with an apology like this?  What if you weren't offended?  What if you were feeling a myriad of other emotions?  I've known of this non-apology apology for a long time and have always felt it's insincerity.  It's in my own personal moral code to always apologize for my actions and take full responsibility for those actions.  I've apologized in the past for something I've done or said where the other party said, "That didn't bother me at all," but my comments or actions bothered me so I felt the need to apologize.  Avoiding situations that end in the need to apologize is the best way to go but if you find yourself in that situation take responsibility, it's cleansing.