Politicians, actors, pop-stars, bloggers for presidential wanna-bes.
Caught with their pants down; saying something outrageous, homophobic, anti-semitic, or offensive in some other way. We see it every day and, with few exceptions, the response is some version of:
"I'm sorry that XXXX was offended by what I said."
That is not an apology. Saying that you are sorry that someone was offended is not the same as apologizing for what you actually said. It is putting the blame on them. Sort of like saying "I'm sorry you heard that and that your skin is too thin to allow you to blow it off."
So, for occasions actually requiring an apology, here's a new one to try out:
"I'm sorry. I was a dolt."
Then you send out your publicist and/or spokesperson and/or issue a press release to let everyone know you are entering drug/alcohol rehab and/or seeking counseling.