When is saying "I'm sorry" the right thing to do?
Whenever you screw up! Especially when that screw up impacts your customers.
It's simply a matter of respect, as Seth Godin points out.
Mmm-hmmm, just a little bit...
If you're having trouble figuring out how to apologize, pick up Ken Blanchard's The One Minute Apology and give it a quick read. It's easy (reading the book and apologizing, I mean).