For a research doctorate a rule of thumb is that an applicant should have at least a gpa of at least 3.4 and decent GRE scores (80th percentile or above) – especially in the quantitative test. It is possible that an excellent GRE score can mitigate a lower gpa. The reverse is not true, as the GRE scores are seen as a more objective measure of intellectual performance than the gpa which might be subject to grade inflation at a particular campus.
For freestanding professional schools (which I address in detail below), which tend to train students in Clinical, Counseling, or Organizational Psychology, the minimum gpa might drop to a 3.2 for fully accredited APA approved schools and perhaps even a 3.0 for non APA approved programs. Likewise GRE score expectations are not as high and there is less emphasis on the quantitative scores.