Though not a sole criterion, the GRE score is an important factors for graduate school admissions. In many “make-or-break†cases, a better GRE score is the deciding factor.
Some universities have minimum GRE score requirements. But there is no hard and fast rule since a GRE Score is not the only factor for evaluating student applications. Along with the GRE Score, other parts of the application (SOP, Letter of Recommendation, Academic background, etc) are taken into account.
Irrespective of what people say, the universities don‘t have a cutoff GRE score. Also, if you come to know that the minimum GRE score required for a certain university is 1300, then it does not mean that you can't apply if your GRE score is 1250. Strong academic credentials and great recommendations can compensate for a lower GRE Score.
If you are aiming for reputed graduate schools, then make sure that you have a great profile. A GRE score above 1500 is will give you a good chance at a top ranked university. A GRE score above 1300 is considered decent for admission to a good graduate school. If you're looking for engineering admissions, then make sure that you do very well on the GRE quant section. For engineering grads, a typical good score (in the GRE quant section) is above 750.
A GRE score of around 1100 will get you admission to a university that's ranked below 50. It's observed that students with low GPAs and average recommendations have to get a good GRE score for admission offers.
Some Universities post last years minimum or average GRE score in their FAQ pages. Be sure to go thru this deciding on where you want to apply.
Average GRE Verbal Score Average GRE Quant Score
MIT 560 780
Stanford 580 780
Berkeley 530 760
Georgia Tech 540 770
UIUC 530 770
Cal Tech 570 800
CMU 550 770
USC 480 750
Cornell 600 770
University of Michigan 530 760
Lastly, don‘t underestimate the importance of a good GRE score!