Th US has completely rebuilt, befriended, and rehabilitated Japan and Germany. We did this despite the horrors their military actions (made up of their citizens, no less) visited upon the Earth.
What more could any rational person want?
If someone is attempting to kill you and your entire civilization; your way of life, it is unnecessary to apologize to their descendants for the destruction you once visited upon their homeland. I cannot see a reason why my distaste for the use of atomic weapons needs to be translated into an official apology by the US.
I certainly don't think it would be enough. As these things go, an apology would end up putting the US in a bigger trick bag. I certainly feel that this is the reason why the question is circulated from time-to-time.
As to the question of war crimes, which has been raised in other answers, maybe. As long as everyone agrees that a single civilian death should be considered a war crime, then certainly any civilian death, no matter how insignificant or catastrophic should be considered the same. Yet, war crimes determination is tricky, and there are rules that many nations have agreed to, when determining what is and what is not. Under those agreed upon definitions, this was untested-uncharted waters. To this day, no one (atomic power) has signed a treaty stating "the use of atomic weapons is a war crime" (as far as my research indicates).
War, it is ugly, and I hate it, but I am glad the US won. Imagine a world where that isn't the case, and it gets scary in a hurry.