Ohio state only requires it if you are going BME. It doesn't require it for the neuro or IBGP ( integrated biomedical). I just checked 2 seconds ago, because I'm applying there and got nervous since I didn't take the GRE.
I haven't come across any school that requires the GRE if you are going for a phd in a standard field as opposed to bioethics, anthropology, etc. But I also haven't looked at every school