For a complete list of the 70 countires that were the Axis & Allies, see the link below. What's interesting are the ones who started out with the Axis, then came to the Allied side. None of the Allies went over to the Axis!
The three major powers in the Axis alliance were Germany, Italy and Japan as they signed a treaty in 1940 that was then followed by other countries joining and leaving including Russia, Hungary, Romania, Bulgaria and other nations.
The Allied powers consisted at first of the United Kingdom, the United States and their allies including France prior to her capture by the Germans. There were a host of other nations that eventually joined the Allies including Canada, Australia, Brazil, the Netherlands, Poland, South Africa, and others.
The Neutral powers were the countries that remained neutral including Switzerland, Spain, Portugal and Sweden.