The number of casualties of this war was tremendous. It is impossible to know how many people exactly died as a result of this war. However, it is estimated that something like sixty million people died. Of these approximately half were civilians because this war included so many bombings and other attacks on civilian areas.
The country that lost the most people was the Soviet Union. It is believed that about 8.7 million Soviet soldiers died along with almost 17 million civilians. China, Germany, and Japan each lost at least one million military personnel in the war. The United States was fortunate in that "only" about 300,000 military personnel were killed in the war. Of course, since the US was isolated from the fighting, very few civilians died as a result of the war.
As noted in the answer above, we will likely never have an exact count, but 60 million is a reasonable estimate.
Some details for you:
Military Dead: 19.0 million
Civilian Dead: 14.7 million
Jewish Dead: 5.9 million
Military Dead: 5.3 million
Civilian Dead: 15.7 million
Total: 55.4 million
These numbers come form the book: The Decline And Fall Of Nazi Germany and Imperial Japan, and frankly I think the numbers a bit low. So, 60 million is a fair estimate.
As a side note, while we are talking numbers....
In World War Two there were 3,363 generals serving in the German armed forces. Of that number 901 died as follows:
Killed in Action: 287
Death Sentence: 25 (German Courts)
Death Sentence: 57 (Allied Courts)
Accidental Death: 49
Natural Causes: 310
Missing in Action: 65
As compared to 166 deaths of German General officers from all causes during the First World War.