Not numerous but specifically Azerbaijan, Kazakhstan, Uzbekistan and Turkmenistan – all four countries speak Turkic languages, and they chose to do so to align

Not numerous but specifically Azerbaijan, Kazakhstan, Uzbekistan and Turkmenistan – all four countries speak Turkic languages, and they chose to do so to align themselves with Turkey. The adoption has been rather slow, and previous Cyrillic based scripts remain in wide use, though. Moldova switched for a similar reason as Moldovans speak Romanian, and they did so to align themselves with Romania. That is a total of five countries. The actual history is rather more nuanced, as after the 1917 revolution, the Bolsheviks – intent, at least in principle, upon eradicating Great-Russian chauvinism and weakening the Russian cultural dominance – introduced the policy of «korenizatsiia», or «nativisation». The new policy encouraged non-Russian populations to cultivate distinct national identities, use their own languages in administration and education and, where indigenous languages had previously lacked established writing systems, develop scripts and literary standards of their own: «Politically and culturally, the nativization policy aimed to eliminate Russian domination and culture in Soviet republics where ethnic Russians did not constitute a majority. This policy was implemented even in areas with large Russian-speaking populations; for instance, all children in Ukraine were taught in the Ukrainian language in school. The policies of korenizatsiia facilitated the Communist Party's establishment of the local languages in government and education, in publishing, in culture, and in public life. In that manner, the cadre of the local Communist Party were promoted to every level of government, and ethnic Russians working in said governments were required to learn the local language and culture of the given Soviet republic»[0]. For that reason, nearly all new writing scripts developed between 1920's and mid-1930's were Latin based. Joseph Stalin, a Georgian himself, ended and reversed the policy in the mid-1930's and instructed the Latin-based scripts to be replaced with the Cyrillic-based ones. [0] https://en.wikipedia.org/wiki/Korenizatsiia https://en.wikipedia.org/wiki/Korenizatsiia