This site has a great page entitled "6 CEO apologies on YouTube".
The companies saying sorry are Domino's, JetBlue, KFC, Mattel, Maple Leaf Foods, and American Airlines.
There's also a link to Amazon CEO Jeff Bezo's apology over the recent George Orwell book scandal involving his firm. I liked what he wrote. It sounded from the heart.
It's interesting to see how differently the CEOs on the page I linked to above, handle themselves.
They range from from stiff and awkward to smooth, to really very genuine.
The Domino's president forgets to look at the camera, which is unfortunate.
Meanwhile the Mattel one has an interesting 'believability' study within it. Check it out.
The JetBlue one is a good example of a convincing and and detailed apology.
No jargon, no mission statements, it's something I'd suggest using in media training in preparation for the unexpected.
Update: Greenbiz has a copy of a letter from the boss of a water bottle company called SIGG that I thought was a useful example too. Here it is. Thanks to Jeff S at Timberland for tweeting it just as I published this posting.