There are tons of study abroad programs which allow students to directly apply to a foreign university (without applying via a US college). Two such programs that I have personal experience with include:
Chinese University of Hong Kong in China
Copenhagen Business School in Denmark
Hope this helps!
My son will be studying in France and Sweden next year through DePaul University. The University of Southern California has a very strong international program in which most students participate. It's a great opportunity to learn the culture of other countries while in school.
Good luck on becoming a study abroad student.
Great question - definitely reach out to your campus' international studies department or academic department, they will give you the best information. I studied abroad during the Fall Semester of my Junior Year and loved the experience.
I was able to go to Florence, Italy and made sure that my classes lined up with my undergraduate requirements. If you or anyone is interested, I recommend asking questions early. I was able to take my fine arts credit while abroad - which involved going to different museums most weeks around the city - defintiely better than spending a semester learning through a textbook!
Hope you get the opportunity!