It’s very simple: if you want to study abroad, you’ve GOT to have a passport. (The obvious exceptions are the BU programs in Washington, DC, or Los Angeles, CA—but it’s still a good idea to have a passport even if you’re going there.)
Many countries require that you have a visa in order to study there. You cannot apply for a visa until you have a passport in hand.
As of August 2013, the U.S. Passport Agency is processing routine applications in approximately 4–6 weeks from the time of application. In order to ensure a more timely delivery of your passport, you should request Expedited Service when you apply. The U.S. Passport Agency is processing requests for expedited service in about 2-3 weeks door-to-door, when overnight delivery is requested and paid for both ways (to and from the passport agency).
Even if you are not sure you will be studying abroad for next semester, you should apply now. A passport is always a good thing to have, and they are valid for 10 years.
For further information and application instructions, visit the State Department’s passport website.