Well, there is such a thing as [Scientists Without Borders](http://www.nyas.org/WhatWeDo/ScientistsWithoutBorders.aspx), but they don’t exactly travel around the world and provide help to people. Neuroscience (like many basic sciences) actually moves rather slowly and incrementally, and they don’t provide direct services to people. Most neuroscientists do domestic research in the U.S. because of the research infrastructure here; if you went to developing nations, it’s unlikely you’d have the infrastructure to get the high-tech equipment you need (like an fMRI scanner). You might be thinking of neuropsychology, but I don’t think there’s a huge demand for neuropsychological services in developing nations. They really need primary care.
There are LOTS of jobs that involve doing development and assistance work in developing countries, though.
If you are interested in health and medicine, think primary care: you can get training in medical school and your MD to do a primary care area (internal medicine, pediatrics, ob/gyn) and do lots of things, like Medecins Sans Frontieres (Doctors Without Borders) or being a medical officer with the CDC or another government agency. You could also get a nursing degree and do nursing work abroad - with the government, with private organizations, with the military, etc. Other allied health careers do a lot of public health work; for example, there’s a desperate need for public health dentists. The U.S. Public Health Service Commissioned Corps is a uniformed service that recruits health care workers and deploys them around the country and world when there’s a need - like after the earthquake in Haiti, or after the Indian Ocean tsunami, or Hurricane Katrina. The USPHSCC hires physicians, dentists, psychologists, nurses, dietitians, engineers, optometrists, rehabilitation therapists, pharmacists, veterinarians, health administrators, scientists, nurses, and other allied health professionals - although for at least the last 2-3 year they have only been commissioning doctors and dentists and occasionally nurses. Still, there are other nonprofits and organizations that would have a need for these alied health professionals in agencies in developing nations. The closer to primary care you are, the better, because that’s where the real need for services are - there’s no money for open heart surgery or extreme brain surgery or something; they need people who are going to administer polio vaccinations and prescribe antibiotics and help deliver babies.
If direct care provision is not your thing, there’s also a need for policy makers: you can go into healthcare administration and help improve infrastructure for healthcare around the world; or you can go into health policy and help shape policies and legislation to improve health on a large scale. There’s also health promotion and education, where you can go into developing nations and do on-the-ground education of people to help improve health. You can major in anything, although a social sceince major is probably best, and then get an master’s of public health (MPH) or a variety of other degrees (MPA, MIA, MPP).
If you don’t need to do healthcare specifically, there are lots of other areas that need attention - like international development and economic policy, international education, environmental health, engineering to improve infrastructure (especially civil engineering), even tech services and such. There are some business folks and economists studying and practicing things like microfinance, for example - small loans to women in West Africa to help them start businesses to support their families. I had a student who was an industrial design major; she wanted to design low-cost toilets for low-resource areas to help women and girls who can’t go to school when they are menstruating because of lack of facilities. I’ve had a student do research on the impact of the Deepwater Horizon spill in the Gulf on low-income communities in Louisiana and other coastal communities (environmental health). A friend (also environmental health) does research on arsenic and other poisons in well water in central Asia, and trains people to educate their communities about how to clean their water. Some people are working on low-cost mobile technologies to help get people in resource-poor communities connected to telecom services; I also know of an educational start-up that designs a technology to help parents in low-income areas help their kids with math. There’s even a group called [Statistics Without Borders](Home - Statistics Without Borders), a volunteer group of statisticians (who have other jobs) who provide free statistical consulting to government and nonprofit organizations in developing nations. Statistical consulting is important for - for example - analyzing national census data to determine population trends and how to distribute resources, plan for population growth, allocate tax revenues, etc.
So…the point is you can go around the world and help people with virtually any major, it just depends on how you want to deploy it. The most obvious and hands-on things are going to be 1) medicine, nursing, and the allied health fields; 2) public health, health education, health promotion, and environmental health; and 3) teaching and education, particularly English as a second language in resource-poor areas.