I think Mark P hit most of the important points on why North Korea's possession of nuclear capabilities is bad. We back South Korea pretty heavily. Even more important it seems to me is our alliance with Japan. Kim Jong Il has spoken aggressively about his intentions for Japan. Japan is a huge trade partner with the U.S.; not to mention we have some very substantial military bases there (oh ya, South Korea as well).
What you don't hear about much is the fact that NK has between 2,000 and 5,000 tons of biological/chemical warfare agents in their stockpile. The more potent materials could be readily put on any of their fully developed missile systems and kill every man, woman, and child in Pyongyang within the hour. North Korea also has alliance with China and Russia. How they would react to a NK aggression like a major missile attack is unknown (to me) but I'd hate to see another world war with one side being those three powers; Russia, China, and NK as allies. Of course China and Russia have their own scruples between each other but extraordinary circumstances birth extraordinary developments.
And as Mark P noted the U.N. and the international community is concerned with Iran having nuclear weapons. Their stance towards Israel is the U.S. primary concern. Of course someone arguing for Iran's case would in my opinion have a valid point if they said "well Israel has nuclear weapons and no one said anything". The double standard is glaring, but if Israel didn't have nukes the tipping point may have come long ago?
All I have to say is get those missile defense systems put up everywhere P.D.Q.!!