STEM applicants may find it much easier to work with the language issue. In most of the world, English is the language of scientific research. Check out this article on STEM-friendly sites.

Finland  offers nineteen grants each year. This year seven of these grants are geared to degree-seeking Master's students - two at the University of Helsinki, two at the University of Turku, and three at the Lappeenranta University of Technology. Its Center for International Mobility (CIMO) also offers five grants specifically for students completing research projects that do not involve course work. 

The Netherlands  offers up to 7 full degree grants every year at one of four universities, as well as multiple research grants. There is no expectation of knowledge of Dutch prior to the start of the grant. 

The European Union  grants, for research into EU institutions or policy-based research in at least two EU member states, frequently have no language requirements for less commonly taught languages. EU grants are more competitive when 

South Korea  offers 10 grants for full Master's programs, taught in English with Korean-language courses, for students interested in Korean Studies. Funding is guaranteed for two years, assuming good academic progress toward the degree. Taiwan now has 5 similar grants for International Studies Master's taught in English.

Hong Kong   offers grants where projects done in English are possible. Malaysia and Indonesia can also support well-designed projects in English.  For countries in Asia that do have less commonly taught languages, Mongolia, Cambodia, Laos, Vietnam and Thailand, some previous study of the language is preferred, but carefully designed research programs can be funded. 

Careful program design can make for a competitive application in sites where English is widely spoken and understood. The nature of your research question and design, however, will determine just how competitive your proposal can be. 

If you plan to complete research in a country where English is not the main language of the country, you must explain clearly how you will work around your language skills, and how you will work to gain language proficiency. If you plan to do archival research, complete interviews, or conduct any kind of research activity that will involve the local language, how will you access sufficient data to make your application competitive without the local language? If you can do this research in using non-local English-language sources, then is your presence necessary in the host country?

Example: Say you want to research Estonia's environmental legislation toward pollution in its fresh-water river systems. It may be possible to design this kind of project in English, as much Estonian legislation is now published in English. Many Estonian legislators speak English well. However, if your interest is in popular attitudes toward Estonia's environmental legislation, it may be much harder to make a convincing case for this project. Legislators and political elites probably speak English well. You cannot assume that random individuals will speak sufficient English to allow you to conduct interview.