On the European front, perhaps the most famous Battle was the Battle of Stalingrad, in which the German advance into Russia was halted. Ironically, the German advanced halted on December 6, 1941, one day before the Japanese bombed Pearl Harbor. Another famous European battle was the Battle of the Bulge, in which German forces attempted to force back advancing Allied forces. It was at this battle that the 101st Airborne division commanded by Gen. McAuliffe was caught behind enemy lines. When asked about surrender, McAuliffe's one word response was "Nuts." Also famous was the Battle of Berlin in which Soviet forces overran the city and Hitler committed suicide rather than surrender.
You might also consider Operation Sea Lion, the German planned invasion of Great Britain which failed and, of course, Operation Barbarossa, the German invasion of Russia, which also failed and which marked the turning point of the European war.
In the Pacific, aside from Pearl Harbor, the two most important battles were the Battle of Coral Sea and the Battle of Midway Island. At Coral Sea, the Japanese forward advance into the South Pacific was saved, as was Australia, which was in close proximity. Interestingly, the entire battle was fought by carrier borne aircraft. The opposing fleets never caught sight of each other.
At Midway, Adm. Yamamoto had planned to intercept and destroy the American fleet which would prevent interference with the Japanese advance. However, Allied forces had cracked the Japanese code and made it to Midway before the Japanese fleet. Fighting was fierce, but Midway marked the turning point in the war. Thereafter, the Allies began a campaign of "island hopping," taking back one island at a time until, ultimately, a choice had to be made between invading the Japanese mainland or dropping the atomic bomb. The decision was made by President Truman to drop the bomb. An excellent source for further information is James Stokesberry: A Short History of World War II.