Study abroad is to college as that trip you took to Washington D.C. is to high school. If you're an international student, maybe there's a better analogy, but the idea is that study abroad is something that you REALLY don't want to skimp out on.
...or at least, I assume so. Right now I'm beginning the wonderfully wonderful process of applying to study abroad programs and hoping for Macalester's approval of my choice. It's already been many an hour of me reading over document after document after page after page of rules, regulations, and requirements.
Nonetheless, it's an exciting prospect. For some majors, like Anthropology or International Studies, studying abroad for one semester is required. But even for people who don't need to study abroad to graduate, it seems a waste of a good opportunity to not go.
What does study abroad give you that travel on your own can not? For one thing, a little structure. To some that may not sound appealing, but some structure (not complete and total authoritarian structure) can help you to get things done and have some experiences that few others can (like homestays, visits to sites, visits to different organizations, and specialized classes). Often times you'll do service learning, or conduct an independent study project. And all of this is facilitated by the program that accepts you, meaning you can focus more on seeing the sights.
You also get a chance to reflect on an almost daily basis with your peers from the U.S., something a trip conducted alone does not provide for. This seems like it would be especially important in places so drastically different from home, like (for me) areas in Africa or Latin America. If anything, you can look at studying abroad as guided touring, but less stringent in your overall path. You can explore a whole new world with some tips and pointers, but in essence it's your experience to have.
Be prepared sophomore year to think about where you want to go. This doesn't mean you have to have a city map charted out; you can settle for deciding on a country. From there you can peruse different organization websites (SIT, ACM, CIEE...) and see what program you like best. It makes narrowing things down a lot easier...
...but no less stressful.