Interestingly, STEM fields are leading the way on this issue. There is a central list for Astronomy/Physics and Bio/BioMed departments (see links below). Please note, some STEM departments require the subject test, but not the general GRE. I am listing mostly departments that do not require either. Confirm a department’s practice before applying by visiting their website.
Help me build this page — what programs did I miss?
Astronomy and Physics:see this (amazing) list of department admissions requirements
Biology and Biomedical Sciences:see this (amazing) list of departments which have dropped GRE or which are planning to do so
Chemistry: Emory; Michigan Technological University; Oregon State University (not req. for domestic students); Purdue; Washington State University (Chemical Engineering and Bioengineering)
Computing and Computer Science: Cal State Long Beach (MA, strongly recommended but not required); Cornell (recommended but not req.); Marquette (optional for admission but req. for financial aid); MIT (Electrical Engineering and Computer Science); Montana State University; Purdue; University of Illinois, Urbana Champaign
Ecology and Environmental Science: Antioch University, New England (Environmental Studies); Cornell (Plant Pathology and Plant-Microbe Biology); Dartmouth (Ecology, Evolution, Ecosystems, & Society); Iowa State University (Ecology & Evolutionary Biology); UCLA (Ecology & Evolutionary Biology); University of Kansas (Ecology & Evolutionary Biology); University of Maryland (Marine Estuary Environmental Science)
Engineering: Brown (ScM/Master in Biomedical Engineering, req. for PhD); Colorado University Colorado Springs (GRE not req. except for applicants not meeting minimum GPA, applying with degree from an ABET-accredited department, and degree from university outside US); Harvard (optional);MIT (Electrical Engineering and Computer Science); University of Idaho (Civil Engineering); University of Nebraska-Lincoln (MEM); Washington State University (Chemical Engineering and Bioengineering)
Mathematics and Statistics: Georgetown (Masters in Math/Statistics); Lehigh University (not required but “helpful”); University of Minnesota (general GRE optional; subject test “strongly recommended”); University of Waterloo Canada; Washington State University (Statistics.)
Psychology/Counseling [not sure where to place Psych! — Stem? Social Science?]: Chicago School of Professional Psychology; Oregon State (Counseling); Philadelphia College of Osteopathic Medicine; Stanford
Other/Interdisciplinary: Rockefeller University; Dartmouth Psychological and Brain Science or Cognitive Neuroscience