If you're taking a position at a big company that is well known in its field, sometimes just having a name to add to your resume is reason enough. The flipside of working with a bigger company is that often interns don't get the experience they are searching for. Many bemoan the fact that they were treated like another piece of office equipment. Discuss your role and duties when you interview for the position. Also, stress to your supervisor that you're eager to get involved.
Enthusiasm is difficult to overlook.
When you consider a pay-free position, also quietly look into the hiring history of the company. This may be tough, but try to find out if the company has a trend of hiring folks when their internship ends. Ask some of the younger employees or other interns that are there. If the answer is yes, seriously factor this into your decision. If you can suck it up and get by for a few months, you might just skip the torturous task of job searching after graduation.