This is a very interesting "counter-factual" question of the sort that professional historians are increasingly likely to ask (see third link below). I find myself in agreement with most of the previous posters. Even if D-Day had not occurred, the Allies had many more resources available to them by 1944 than the Germans had. In addition, of course, the United States was well on its way to developing the atomic bomb, and that weapon may have been decisive in ending the conflict even if D-Day had not taken place. It's always worth remembering, too, that there were an astonishing number of assassination attempts against Hitler during the twelve years of his rule. Some of them came very close to succeeding. Surely someone in the German high command would have seen the wisdom, at some point, of assassinating Hitler before Germany was bombed with an atomic weapon. (I may be too optimistic, however, in assuming this.)
As it happens, your question has been discussed elsewhere. Here are some interesting links:
It is always very difficult to hypothetise about how things would have worked out had history been different. However, it does seem that given the position of the two opposing sides at this time, it was just a matter of time until Germany had to reconcile itself to defeat. D-Day obviously accelerated this process, but there is no way in which we could argue the absence of D-Day would have given a different result.
The reality is it's hard to say. According to Churchill, the allies didn't want to invade through Italy because the Alps are in the way and the going would be too tough. The question, though, is about D-day...not about an invasion of France. Some argued for and invastion through Southern France using Free French troops from Africa.
Interestingly, it was Stalin who pushed hard for D-day to occur. Again, according to Churchill, Stalin felt that having the Brits/Americans invade from the west would give his troops the morale boost that they needed to keep on fighting. He was very worried that if another front didn't open up that he would have to pause in his push toward Germany. On the other hand, Stalin also admitted that the simple threat of invastion in northern France tied up significant German forces that could have been used against the Soviet Union.
I don't think a negotiated settlement was possible at this point; Hitler had done too much damage to Europe to ever allow him to remain in power and he would have never negotiated anything that didn't allow him to stay there. In addition, had he not provided the German people with the ultimate victory he had promised them and settled for a reduced Germany to stop the war it is likely the National Socialists would have been driven from power.
As others have said, the war probably would have gone on a little longer as the Russians took time to shore up their supply lines and regroup, but they were on a roll and would have plowed Germany up eventually even without our help via Normandy. They would have then established a "sphere of influence" even larger than the one they really got after the war.
Mostly, I think the absence of a D-Day invasion of France would have resulted in more Soviet influence in postwar Europe, but as others here have stated, Germany was already doomed to defeat by June of 1944. The final collapse of Germany came a mere 11 months later, and was due less to the Allied invasion than it was to the Russian juggernaut in the East. Strategic bombing of Germany would never have been enough on it's own to have resulted in a German surrender.
I agree with the two previous posts. The war would have been a lengthier one, but Germany would never have been able to hold out against the combined Allied forces advancing from Italy and the Russians moving in from the east. Hitler would have eventually have been defeated or may have actually consented to a negotiated truce at some point, but it would have been one similar to that of World War I, which left Germany with fewer of its lands.
If D-Day had not happened, the war would have been prolonged; but the end result would have been the same. Hitler grossly miscalculated by invading the Soviet Union; he could have devoted more of his troops to slowing the Soviet advance from the East; but with weakened German forces and the T-34 tanks which were virtually unstoppable, the Soviets would have prevailed. In terms of later years, it is highly likely that Berlin would have been completely occupied by the Soviets, and all of Germany as well as the entire city of Berlin would have been part of the Soviet Bloc.
One must remember that General Patton's forces were proceeding up from Egypt into Sicily and Italy. Even without D-Day, it would have been impossible for Germany to win the war.
I do not see how WWII in Europe could have been won without an invasion of France. Therefore, without D-Day, there would presumably have been a negotiated peace between the Allies and the Germans.
Without an invasion of France, the Allies would have been pressing in from Italy and from the East. However, with no D-Day, the Germans would have had many more men and weapons available with which to resist these pushes. The move up from Italy would have been very difficult because of terrain and would likely not have put that much pressure on Germany.
I do not see how the Allies could have defeated Germany in any kind of timely way without invading France.