Talk to your department at school about possible research grants. Sometimes there are unlisted opportunities saved for faculty members, graduate students and extremely dedicated undergraduates. In order to get the most money, develop a relationship with a faculty member who travels often. This person could also help you find cheap housing and airfare.
Shortly after World War II, the Rotary Foundation began granting scholarships to promote international understanding. Now, the foundation grants study abroad scholarships to hundreds of students per year. There are separate opportunities for graduate and undergraduate students.
Honor society chapters have grants available to members and nonmembers. Examples include the Phi Kappa Phi grant, open to any majors and the Sigma Theta Tau grant, intended for nursing students. The applications for these grants are extremely competitive and require a flawless academic record.
Fellowships are generally for graduate students, especially those working on research. Fellowships are available from a wide variety of research foundations, nonprofit organizations and universities. One of the most prestigious study abroad fellowships is the Fulbright Grant.
A great resource for students looking for free money to travel is studyabroadfunding.org. The website lists available funding by destination, level of study or major.