Readers depend on news websites to report breaking news in a timely manner. I'm sure CNN would love to have a full article about the charges as soon as they are announced, but even they need some time to read, digest, and write up their report.
I'm a bit puzzled. "Breaking" doesn't mean "important". In this context, "to break" means:
14. (v. tr.) To make known, as news: break a story.
15. (v. intr.) To become known or noticed: The big story broke on Friday.
(http://www.answers.com/topic/break)
So a "breaking news" story is one that is being made known or becoming known. In the morning when the story was becoming known, I think the label was perfectly appropriate.
Did cnn.com really "interrupt" any "scheduled" programming with the Cuban story? They usually just have that red bar over the top with the "breaking" headline.
Obviously the definition doesn't transfer perfectly to the internet.
Traditionally breaking news is reserved for news deemed important (see previous definition). The problem is, everyone uses it too much, and if too many things are deemed important, nothing is. And we're back to where we started :).
