In addition to the turning points that I mentioned in answer to your other question, here are some major battles:
- The Battle of Britain. This was an air battle over a number of months. In this battle, the German Luftwaffe tried to destroy the RAF and/or defeat the British by bombing their cities.
- Guadalcanal. This was a major battle between Japan and the US to control this strategically important island.
- Saipan, Iwo Jima, and Okinawa. These were huge battles that happened as the US fought its way towards the Japanese mainland.
- D-Day. The invasion of the European continent in June of 1944 was a major battle and opened a western front that threatened Germany. The success of the landings essentially doomed Germany.