I know that in most U.S. universities, most programs for graduate studies require a GRE score.
1- Are there any graduate programs in the U.S. which does not require this?
2- Is it required for graduate programs in Europe, Australia or other parts of the world?
I've studied in Australia and the U.K., and I believe that no universities require GRE for graduate admission. I don't believe that GRE is required in continental Europe either, but there may be exceptions.