There are a lot of reasons to do it. When else in your life will you find another stretch of several months in a row where you can pick up and move to another country without losing ground with your job, education, etc.? In college seems like the perfect opportunity to do it. You can entirely immerse yourself in another culture, another city, another language (if that's your thing). Rarely is a vacation to a foreign land really sufficient to experience this kind of immersion. You're young. You're adventurous. I'm a big believer in gulping life (rather than just sipping it) and studying abroad is yet another way to do this. Several people I know who did it in college reflect on that time as one of the best experiences of their lives.
All of that being said, I have to admit that I didn't choose to do it. My lovely wife (before we knew each other) didn't do it either. And our reasons were pretty much the same. I was having too much fun in college and it seemed to be going very quickly. By the end of my sophomore year, it dawned on me that I only had 4 more semesters as a college student and there were still so many things at my school that I wanted to do. I don't regret my decision. I had a blast those last 4 semesters. And since then, I've done a fair amount of traveling. I feel like I've gotten my fair share of other cultures.
Now that my son is a sophomore in college, the conversation occasionally rolls around to studying abroad. We encourage him to go if he wants to, but also tell him that we would understand if he chooses not to. He has traveled extensively even though he is only 19, and we believe those travels have ingrained in him a deep curiosity about, and appreciation of, how other people in the world live. If my wife and I had regrets about not going ourselves, we would probably encourage him more strongly. But he's a smart, creative and responsible person who will ultimately make the right decision for him.
Would be curious to hear what people felt about their study abroad experiences (or decisions not to go).