I just left a lengthy comment on Erika's blog, so I thought I'd post it here, too, since I love to get as much mileage out of stuff as possible!
I firmly believe in teaching children how to correctly apologize. We developed a formula for our family before they could really begin to talk. Step 1: "I'm sorry for [verb+ing]" Step 2: And here's where Ray and I differ-- Ray's:"I will not do it again." Mine: "I will try my best not to do it again." (There's a continual discussion of which is more appropriate.) Step 3: "Please forgive me." Step 4: response: "I forgive you." (VERY important here b/c we noticed that so many times when someone apologizes the other person just says "It's OK," as if to shrug off the validity or the severity of the trespass.) Step 5: Hug or physical connection.
It seems to work well. The kids need coaching sometimes, but overall they've acquired the skill of a sufficient apology. Merely saying "sorry" in my house doesn't cut it! I'm hoping this helps them when they reach the age of reason and must make a good confession.
I've always struggled with receiving the false apology, (pointing finger here at others' failures,) "I'm sorry you got upset..." Insult to injury! Now, there was one time that I thought it ROCKED. And that is when Pope Benedict XVI offered the false, but necessary, apology to the unfoundedly inflamed Muslim community about his comments at Regensburg, "I'm sorry that my comment upset you." Now that's the Holy Spirit!