Most NGO positions require people with degrees in the function they will be performing and not in NGOs. Non-profit administration and International Relations are two generalist degrees that come to mind. International Humanitarian Law is another.

People who work in the NGOs usually have to be experts in whatever their function is. They are accountants, engineers, teachers, social workers, nurses, etc… and need their degree in those fields. A minor in area studies or culture of wherever they want to serve can be useful. If you plan to serve internationally, language skills are essential. French and Spanish are very common requirements.

One way to understand what different agencies require of their employees is to search their web page for position openings that you'd be interested in.

?????? Non-Government????

The only thing this makes me think of is non-profit. Which to work for these types of companies you can study just about anything.

Little money, makes me think of shelter jobs, mental health agencies, etc. There you would need a degree in a social science. Preferably a Social Work degree.