Don't make public apologies.
If your indiscretion was premeditated, the apology rings hollow. It's more of a "Sorry that I got caught" message. Druggie ballplayers are famous for this as are philandering Democrats and homo Republicans.
If you spewed out something and it wasn't taken too well, apologizing only weakens your credibility. Either you were rash, drunk, or misinformed, when you made the statement; or if not, you are caving into pressure and abandoning your principles. Stick to your guns if you are right. If you pulled the opinion out of your butt, make a note to yourself to think before you speak in the future
If you truly screwed up, and did so unintentionally, apologize in private to those directly harmed by your words or deeds. The whole population is not entitled to your display of remorse. I sure as hell don't want to hear it.
Seems like every day someone is apologizing to the masses. Why am I offended that someone bought sex for $4000 a pop? Obama's a black guy. Hilary is a female. McCain is 72. Should anyone have to apologize for pointing out these facts?
Just once I'd like someone to say, "I said it. I meant it then and I mean it now." or better yet, "She was worth every penny."