I want to say it's unfair, but I can't.
Typically, how much a grad school cares about GREs in relation to admissions is inversely proportional to their quality.
Generally speaking, top-tier programs set a GRE requirement for that year's admissions to cut down on the number of applications they have to look at. If you fall below that, you could still get looked at if they end up having the time to do so, or if you pester them a lot/have some pull within the department (it's not super uncommon for a professor who will give you a recommendation to also give your target university a heads-up, if they know someone there. This only really applies if you are coming out of a quality undergraduate program, though). After that, your GRE scores mean nothing--you are going to be judged entirely on the quality of your application, with the vast majority of attention going to your writing sample and recommendations. GPA falls into the same realm as GRE scores (and even then, the hard minimum is usually only for your major discipline GPA).
If your application gets looked at, it's practically unheard of for them to reject you on basis of your scores. They need to be really stumped on deciding between two candidates to do so (and in those cases, they'll often just admit both).
As the quality of the program goes down, however, more importance is placed on your score. They need the press from having the highest GRE classes they can get, and their applicants are generally of a lower caliber than the better programs in the first place.
Once you leave this tier behind, you've reached fairly low quality schools. Now, that doesn't mean that they are bad programs--if you are going for something more practical than academic, they don't necessarily need to care about prestige. But, even then, most schools would probably demand their applicants take the GRE.
I've honestly never heard of a program that doesn't. But they could be there. But they definitely aren't at the high or middle tiers of academic programs.
Anyways, you all are horrible, @#%^ed up people
Never underestimate the healing power of a massive dong.