Virtually every country was involved. Not all participated in the fighting, many like France fell to the Nazis early on. Some remained neutral or came in on the side of the Allies as the war was ending in order to secure a place in the United Nations that emerged after. The actual fighting was relatively limited - only the USSR had fighting on its home territory although the UK was bombed repeatedly by the Luftwaffe and the V1 and V2 Campaigns.
Theaters included North Africa, Asia, The Middle East, The Far East, the Pacific and Atlantic Oceans. There were hundreds of declarations of war in the period - with Italy changing sides to join the Allies against Germany.
There were some wars fought separately from the main events such as the war between Finland and Russia, and the Anglo-Iraq War but inextricably tied up with the global conflict.