Master's degree in Public Health from the University of Arizona. While an extraordinary profile can work without a GRE score, an average profile is reinforced with a GRE score. As can be seen from the list, for each university that has waived its GRE requirement, there are many universities that still explicitly require GRE scores from their applicants. You must mix and match schools that don't require GRE at all (and that won't consider the GRE score, if presented) and some GRE optional schools.
In very simple terms, applicants without a GRE score can only apply to universities that have waived their GRE requirements. A candidate without a GRE score is automatically disqualified by other U.S. universities that require a GRE score. If you decide to take GRE and score well, there is a higher chance of getting merit scholarships, as most of your competitors will decide to apply without GRE, and your high GRE score will stand out among your competition.
So, if you haven't applied for GRE or if you have average or below average GRE scores, making the final college list will be difficult.