A professor that I did undergrad research with actually got an article published in Science on the subject. He did a huge meta analysis of scores of admissions tests for various disciplines (GRE, MCAT, etc) compared to various measures of grad student performance (publications, grades, time in school). He found that these tests were actually pretty good predictors, with correlations between .3 and .5. They aren't the best, but they're decent predictors of performance and the best we've got.
That being said, everyone still hates taking them.