I am studying abroad in Copenhagen, Denmark and would like to travel during my semester abroad. I do not know the exact days and places that I want to visit though. Should I get a railpass? If so, what kind?
If you are going to school in Copenhagen there will be school holidays during which you can travel. Wait until you have a term or class schedule and then plan your holidays around that. You can buy more economical tickets with that information than if you buy a railpass. Just have a look at your holidays and buy the tickets as far ahead as you can. There may be a possibility you can get some kind of student discount. I don't know the details but we have seen hundreds of students traveling around Europe on trains during school holidays.
Thank you for the advice! It has definitely helped me in making my decision.
You might do better to look at low cost airlines and ferries. Rail travel from Copenhagen is really only convenient to the rest of the country, southern Sweden and perhaps the far north of Germany. For example, it's a 7 hour train ride to Berlin and 5 hours to Hamburg, to get some perspective. As a student, you are probably eligible for different types of transit passes. See what's available once you arrive. Don't even think of using a 3rd party agency in the US.