In World War I, why did Romania, Greece, and Montenegro decide to go on the Allies side, instead of on the Central Powers side?

This is such an extremely-complicated subject that it can't be adequately answered in a context like this. Historical territorial claims were at work, among other things, but I suggest that you start with a site like the one below and work your way through the links and related sites:


https://en.wikipedia.org/wiki/Allies_of_World_War_I

Agreed. Romania in particular had vast territorial claims on Austria-Hungary - Transylvania, the Banat, Bukovina and various bits and pieces. Greece had various claims against Bulgaria and fears about Bulgarian plans to conquer Macedonia as far west as Like Ochrid.

It should be said that the main enemy of all of these countries was Turkey. Turkey was an ally of the central powers. Montenegro had fought the Turks in both of the Balkan Wars, as an ally of Serbia. As a reward they received half of the sanjak (Turkish district) of Novi Pazar in 1913. As a result of this alliance the country supported Serbia against the Central Powers in WW1. Romania was neutral in WW1 until 1916 when it entered the war on the side of the Allies. As a result of this they gained Bessarabia, Transylvania, Eastern Banat and Bukovina. Greece entered WW1 against the Central Powers in 1917. In the Balkan Wars (1912-13) the Greeks had gained some Turkish territories, and the war with Turkey continued after WW1 (1920-22).