The American Mathematical Society has a scholarship program specifically for the Math in Moscow study abroad program.
The Gilman Scholarship is a nationally competitive scholarship that students with economic need can apply for for research or study abroad.
The Boren Scholarship is a nationally competitive scholarship that any student can apply for to do research or study abroad in countries excluding Canada, Western Europe, Australia and New Zealand. Note that language study and future government service are part of the commitment.
UA's Office of Nationally Competitive Scholarships regularly holds information sessions and provides information and assistance with scholarships like Gilman and Boren.
The DIMACS REU has an annual trip to Prague, Czech Republic that a few select students from the REU may be selected to attend. DIMACS is a paid Research Experience for Undergraduates, funded by NSF. Projects typically relate to math and computer science.
The Amgen Scholars program provides funding to participate in research at a US institution. There are many summer Research Experiences for Undergraduates (REUs) available each year; we maintain a partial listing on our website.
Some countries have scholarships to study or work specifically in their country.
Example: Germany has a DAAD Scholarship for undergraduate students