For the majority of programs, the GRE is required, but there are the occasional few that don't have a standardized test requirement. A few schools are even accepting the MCAT now as well! But anyways, this is not an all-inclusive list at this point, but thanks to Christina K., here are some of the schools that don't make you take the GRE!

Emory University - Georgia
Stony Brook University - NY
Drexel University - Philadelphia
Thomas Jefferson University - Philadelphia
PCOM - Pennsylvania
Hofstra University - NY
New York Institute of Technology - NY
Rutgers - NJ
MCPHS University (Boston)
Mercy College - NY
Loma Linda University - California
Arizona School of Health Sciences
University of South Dakota
Western University of Health Sciences - Oregon
Eastern Virginia Medical School
Howard University - Washington DC