Before I start, let me say I voted yes.
But in reality, it's too hard to tell. We've had all sorts of discussion and debate on this topic in school, and the only conclusion I've come to is that you can't make one. Major events in history like this are just too hard to make a "what if?" situation for. You can't just isolate one little thing like this and expect everything else to be the same. There are too many variables. So in other words, I really dislike playing with "what if?" scenarios unless it's just for fun.
So then, here are the points:
Against: Japan was rotting on the vine. Several months of American blockade and incessant bombing were taking their toll. At first, it was "just" B-29's making firebombing raids every few nights. But by the end of the war, Japan's military had been so thoroughly devastated that American aircraft carriers could safely come close enough for carrier aircraft to attack the Japanese mainland. Japanese war industries had ground to a hault. There was almost no fuel and no raw materials left, not to mention almost no trained & experienced pilots, soldiers, and sailors, and not much population left to draw on. There is now strong evidence that the emperor and several of his closest advisors were preparing to surrender, no matter what the war crazed military would say. If I am correct, the emperor actually had already recorded a mesasge to announce their surrender when the first bomb was dropped. Furthermore, just a few days before the bomb was dropped, the USSR entered the pacific campaign and began to vigorously fight south into Manchuria, and probably wouldn't have hesitated to go straight to Japan.
In short, those against the bomb say that Japan was already on her knees, and if she had been given a better chance to surrender (instead of "unconditional", allow them to keep their Emperor), she would have.
For: Although Japan was militarily on her knees and by all means had already lost (except they didn't admit it), they still had an incredible fighting spirit. Japanese military leaders called for all men, women, and children to meet the American "devils" on the beaches with any weapon they could find and fight to their "honorable" deaths. A few weeks ago, my history teacher showed us a Japanese propaganda film showing a Japanese military rally, where people cheered vigorously as they sent off 13-14 year old boys to fight. The main speaker gave a speech about fighting to the death and making the ultimate sacrifice for their Emperor. A chilling sight, indeed.
Also, Russian entry into the war would only serve to cause further conflict, not a solution. It is because of the Russian entry that Korea was "tempoarily" divided into Communist north and Democratic south, and to a lesser extent that Mao eventually defeated Chiang Kai Shek (sp?) in China. If Russia were to have assisted the US in an invasion of Japan, it is doubless that today we would have the same, a north and south Japan. This kind of seperation has caused nothing but suffering for countries that have endured it (Germany, Korea, Viet Nam).
So, in short: The bomb was necessary to quickly end the war, saving millions of American and Japanese lives, as well as preventing a split of Japan and halting postwar Communist influence.
As I said before, you really can't tell though. What if Japan's citizens disobeyed their call to suicide and demanded the Emperor to surrender? What if the military coup that almost brought down the emperor when he tried to surrender had succeeded? What if the bomb failed to go off or did not have the great effect we had hoped for?
Man, I'm such a nerd. THIS is what AP history classes do to you!