It's an unfortunate fact that people in the sciences tend to be more likely to get paid positions as an option. The companies and organizations offering them have more money to spend, and can afford to pay their interns better. People in the arts are least likely to be able to land a paid internship, and there will be a lot of competition for the ones that exist. Keep this in mind when you make your decision. The field you work in is going to seriously affect whether a paid position or an unpaid one is right for you.
That said, if you can afford it, don't rule out unpaid work. That's because the paid positions will be the most in demand, and you'll have less of a chance of getting them. Plus, just because an organization doesn't have the ability to pay doesn't mean that it can't offer you a lot. After all, you're getting into an internship to learn, not to make money. A group that can't offer you a wage for your work can still give you important training. Plus, they might even be more likely to give you good work - it's a way of compensating for the lack of pay. So you'll learn faster.
You'll also benefit from making friends and learning names. This can give you the contact information and references you'll need for a well paying job later on. Do the best job you can, even if you're not getting paid, and you could end up getting a better professional position once you graduate. There are plenty of things that you can get out of a position, even if money isn't one of them.
Not everyone can afford to take an unpaid internship. Many students are working to get themselves through school already, and can't take on an extra job with no compensation. If you're one of these people, you'll probably need to look only for paid opportunities. However, if you can work just a few hours a week at an unpaid position, you'll be getting valuable experience.
If you don't have to work full time to get yourself through college, or if you have help from relatives, you should take any opportunity you can find. Choose the organization that'll give you the best work experience, not the one with the highest paycheck. It'll pay off again later on. If you have to choose a time in your life to make very little, college is the best one. An unpaid opportunity now can give you a real leg up later in life.