I have been asked this question many times. The short answer is, "Maybe." The long answer? You have to meet five tests for claiming a dependent. One of those tests is the relationship test. You must be related to your dependent by blood or marriage. Or the person must live with you as a member of your household for the entire year. If you supported your roommate while she was looking for a job, that's very generous of you. But you don't get to claim her as a dependent unless she lived with you from January 1 to December 31.
Dependents - Tax Topic 354.