European Theater:

The “Battle of France” at the beginning of the war, which ended the period known as the “Phony War”. First historical instance of the Blitzkrieg tactic.

The “Battle of Britain” in which the British held off the Luftwaffe and survived as a nation long enough to bring in more help.

“Battle of Moscow” which kept a large chunk of the German army tied up and eventually ended up with them having to fall back.

The “Allied invasion of Sicily” which eventually lead to the King of Italy dismissing Benito Mussolini and making peace with the Allies.

And, of course, the “Battle of Normandy Beach” which led to the Allies gaining a foothold in France and eventually defeating Germany.

Pacific Theater:

We can’t have a list of important battles without including the first one, the “Battle of Shanghai”, in which the Chinese and Japanese took what was a low-level conflict and raised it to the level of total war. We tend to ignore this battle, because we weren’t in it, but a three-month long battle with over a quarter million casualties seems pretty important to me.

Then we have the attack at Pearl Harbor, which brought us into the conflict.

There’s the “Battle of the Coral Sea”, which effectively halted the Japanese military expansion, and the first fleet action in which aircraft carriers engaged each other. It was also the first naval battle in history in which the ships neither sighted nor fired directly upon each other.

It was followed closely by the “Battle of Midway” which was a decisive victory for the US, and permanently damaged the Japanese Navy’s ability to go on the offensive.

While the battles for the various islands were both important and bloody, the Battle of Iwo Jima and Battle of Okinawa were probably most important, as they were on Japanese territory, and brought US forces close enough to hold bombing raids over the main Japanese islands.

Hope this helps.