World War 2 is often recalled as being a war between the Axis (Germany, Italy and Japan) and Allies (Britain, USA and USSR). While this is not necessarily inaccurate it can be misleading, for in truth a far larger number of countries were involved. By involved, I refer to countries that made a significant enough military contribution to be on a war footing between 1939 - 1945. As such countries like Denmark and Belgium, with their neutrality violated, I do not consider to have been involved in military terms. So, here is the list with a brief narrative for each:
Albania: Invaded by Italy in 1939 but provided strong resistance up until 1940. Albanian nationalist groups continued to resist and in 1944 removed German troops from the country. The only eastern European country to do so without Soviet assistance.
Australia: Committed to war against Germany in 1939 in conjunction with Britain. Proved more useful in Pacific theater against Japan. Australians fought in Malaya, the Dutch East Indies and the Australian territory of New Guinea. The Australian mainland also came under attack by Japan.
Bahrain: The Sheik of Bahrain declared war on Germany in 1939. Bahrain forces fought under British command in the Middle East theater.
Canada: A Commonwealth nation. Main military contribution made during Operation Overlord, where Canada provided troops and military equipment. Also assisted in North Africa.
China: Invaded by Japan and defended against Japanese invasion forces.
Egypt: More of a battleground in North Africa, but did provide some naval support to Britain and US.
France: Like Britain, went to war in defense of Poland to form a Anglo-French alliance. Unfortunately, despite having a sizable military, was invaded and defeated by Germany in 1940 due to technical limitations and poor strategy. French resistance, forced underground, continued throughout and up until the liberation of France in 1944.
Great Britain: Great Britain represented two entities. Firstly the U.K., and secondly the U.K. along with associated Commonwealth (empire) nations. Went to war with Germany in 1939 after German invasion of Poland. Still boasted world's largest navy in 1939 in addition with a mobile and technically advanced air-force spearheaded by the RAF spitfire, which was crucial to the defense of the British Isles after fall of France. Land army more limited in comparison to Germany, but improved in time for D-day in 1944. Most successful in North Africa, winning a significant battle at El-Alamein. In conjunction with American partnership, this enabled the defeat of Fascist Italy. Also tried to assist within the Pacific theater, where British forces and colonies were largely defeated and captured by Japanese troops.
Greece: Attacked by Italy, but was able to defend against and defeat Italian forces in 1940. Defeated by Germany who occupied Crete after some resistance.
Holland: Quickly defeated by Germany in 1940 within 5 days. Became an occupied country, and later liberated in 1944.
India: Another Commonwealth nation who fought for the British Empire, mainly in North Africa and in the Middle East against Iraq.
New Zealand: Member of the Commonwealth club, which declared war on Germany in 1939. Provided military support in Europe and Pacific.
Norway: Located near to Sweden and German oil supplies, invaded in 1940 by Germany against Anglo-French troops. Defended but was defeated and became occupied.
Poland: The first nation invaded by Germany in 1939. Likewise, quickly defeated and became occupied. However, Polish air-fighters also engaged the German air-force in defense of Britain - with distinction. Liberated by USSR in Eastern Europe during the Soviet advance towards Germany 1944-45.
South Africa: A Commonwealth nation, which assisted Allies in Europe with several divisions.
USSR: The Soviet Republics, backed largely by mother Russia. Probably the most militarized country in 1939; signed pact with Germany in 1939 and occupied parts of Poland. This did not last, and the subsequent German invasion in 1941 brought the USSR on a full war footing against Germany. Forced back initially, but launched strong counter offensives and big defeats on Germany at Stalingrad and Kursk; eventually, moving out of USSR into Eastern Europe and Berlin. Also attacked Finland in an attempt to gain territory. Ultimately, victorious against both countries despite heavy losses. Later joined war against Japan in 1946.
USA: The United States of America. Isolationist until bombing of Pearl Harbor in 1941, America assisted the Allies' war effort considerably up to 1945 by aiding Britain and the USSR. Defeated Japan in the Pacific, and made considerable contributions in defeating Germany and Italy with American troops occupying both countries in 1943 and 1945 as part of Operation Overlord and Operation Torch. German U-boats were also defeated in the Atlantic by the USA in 1943.
Yugoslavia: A Balkans nation that Germany invaded for strategic reasons. Resisted, but was defeated and occupied.
Bulgaria: Regarded as an Axis nation, and supported the German invasion of USSR. However, later declared war on Germany in 1944.
Finland: Regarded as Axis largely because of war with USSR. Entered war in 1940, when attacked by the USSR over territory demands. Provided strong resistance until finally defeated in 1944.
Germany: Regarded as the strongest Axis country. Started war in 1939 by invading Poland and defeated many European nations, including France. Unable to defeat Britain, USA and USSR who defeated the German invasion attempt on Russia and later occupied Berlin. Also assisted Italy in North Africa, but defeat at El-Alamein forced their withdrawal. Defended against Operation Overlord in 1944 but lost to the Allies. Their defeat led to the Axis defeat, and Germany became an occupied country by surrendering in 1945.
Hungary: Hungary was a significant German ally throughout the war and signed the Tripartite Pact in November 20, 1940.
Italy: Entered the war in 1940, but lost battles against Britain in North Africa, eventually calling on German support. Invaded and defeated by Allies during 1943-1944 as part of Operation Torch. Also provided troops for invasion of USSR.
Romania: Supported Axis as a result of Soviet demands to Romania territory in 1940, and provided military support to Germany on eastern front. Also had important oil supplies located in Baku.
Japan: A military dictatorship and only Axis nation in the Pacific. The Japanese Empire launched a most effective airstrike on Pearl Harbor in 1941 to bring the USA into the war. Swept through the Pacific with numerous victories, until the naval defeat at Midway forced them into retreat and ultimate defeat by 1945. Forced to surrender after nuclear attack by the USA.
These were the nations that were really involved in a military sense. Other nations like Iraq did engage militarily but were so unreliable, partly siding with Germany and then being forced against them, that it's difficult to include them as Axis or Allies. Needless to say other countries like Belgium, Denmark and Morocco, although involved in a strategic sense did not actually provide a military contribution (trying to stay neutral) and should not be included here.
Evidently the Axis defeat is perhaps not surprising with the larger number of Allied nations involved, with Britain and its Commonwealth club alongside the military might of the USA and USSR. Equally the Allies were a more cohesive alliance than the Axis, which gradually broke up as the defeat of Germany and Japan became likely.