Neuroscience:
Neuroscience Information Network - The Neuroscience Information Network is a National Institute of Health project. It provides access to a variety of neuroscience resources.
The Society for Neuroscience Press Room - The Society for Neuroscience, or SfN, is the nation's largest neuroscience group; it has over 40,000 scientist members. The Press room section of their website has a variety of articles on recent breakthroughs in the neuroscience field. 
The Society for Neuroscience - Public Education - SfN also has a number of large public outreach initiatives, including its Brain Awareness campaign. 
The Human Connectome Project - The human genome has been mapped; however, the connectivity of the brain hasn't! The Human Connectome Project aims to map how different areas of the brain are connected to one another. 

Drug abuse and addiction:
The National Institute of Drug Abuse (NIDA) - Latest News - NIDA posts articles about the latest findings in addiction research. 
NIDA - For Teens - NIDA has a website aimed at explaining the science behind the effects of drugs on the brain in teenagers.
NIDA - Information for Patients and Families - General information about drug abuse and treatment for patients and families from NIDA.
NIDA - Information for Parents and Teachers - General information about drug abuse and treatment aimed at parents and teachers. 
Rethinking Drinking - Rethinking Drinking is a website designed by the National Institute of Health. It explains serving sizes for different types of drinks and provides other alcohol-related resources. 
National Institute on Alcohol Abuse and Alcoholism (NIAAA) - The NIAAA is associated with the National Institute of Health and provides information about alcohol abuse.
QuitAlcohol.com - This website describes what alcohol does to the body.