Accelerate Cures for Patients Act of 2009 - Amends the Public Health Service Act to authorize additional appropriations to the National Institutes of Health (NIH) to conduct or support medical research that relates to cancer, cardiovascular disease, diabetes, Alzheimer's disease, Parkinson's disease, or other diseases or conditions and that has the greatest potential for near-term clinical benefit in human patients, as indicated by substantial evidence from basic research or by substantial clinical evidence. Allows such evidence to include: (1) evidence of improvement in one or more human patients suffering from illness or injury, as documented in reports by professional medical or scientific associations or in peer-reviewed medical or scientific literature; and (2) approval for use in human trials by the Food and Drug Administration (FDA).