Here are the countries that participated World War 2 but didn't joined the Allies, or eather Axis (even that most of the countries on this list actually joined the Allies some years later)
Official Belligerents:
Union of Soviet Socialist Republics
Сою́за Сове́тских Социалисти́ческих Респу́блик
Joined the war on: 17 September, 1939
Byelorussian Soviet Socialist Republic
Беларуская Савецкая Сацыялістычная Рэспубліка
Белорусская Советская Социалистическая Республика
Joined the war on: 17 September, 1939 - Non-Official Belligerant - Republic of Union of Soviet Socialist Republics
Ukrainian Soviet Socialist Republic
Українська Радянська Соціалістична Республіка
Украинская Советская Социалистическая Республика
Joined the war on: 17 September, 1939 - Non-Official Belligerant - Republic of Union of Soviet Socialist Republics
Republic of Finland
Suomen tasavalta
Joined the war on: 30 November, 1939
Provisional Government of Lithuania
Laikinoji Lietuvos vyriausybė
Joined the war on: 23 June, 1941
Ukrainian National Government
Українське Державне Правління
Joined the war on: 30 June, 1941
Imperial State of Iran
کشور شاهنشاهی ایران
Joined the war on: 25 August, 1941
Ukrainian Insurgent Army
Українська повстанська армія
Joined the war on: 14 October, 1942
First Czechoslovak Army in Slovakia
Prvá československá armáda na Slovensku
Joined the war on: 29 August, 1944
Puppet States:
Finnish Democratic Republic
Suomen kansanvaltainen tasavalta
Joined the war on: 1 December, 1939 - Puppet State of Union of Soviet Socialist Republics
Estonian Soviet Socialist Republic
Eesti Nõukogude Sotsialistlik Vabariik
Joined the war on: 7 July, 1940 - Puppet State of Union of Soviet Socialist Republics
Latvian Soviet Socialist Republic
Latvijas Padomju Sociālistiskā Republika
Joined the war on: 7 July, 1940 - Puppet State of Union of Soviet Socialist Republics
Lithuanian Soviet Socialist Republic
Lietuvos Tarybų Socialistinė Respublika
Joined the war on: 7 July, 1940 - Puppet State of Union of Soviet Socialist Republics
Questionable Belligerents:
Republic of Latvia
Latvijas Republika
Latvejas Republika
Leţmō Vabāmō
Was invaded by the Soviet Union: 16 June, 1940