I kinda boggles my mind that they allow calculators on the SAT now. Some googling indicates that they are still prohibited on the GMAT.
I can confirm that. No calculators on the GMAT (at least when I took it 2 years ago).
Calculators haven't been allowed on the GRE either but with the new one (it either started this month or next month), they are offering an on-screen calculator built into the test.
Yup. You could make a decent argument that a graphing calculator has been marginalized into a $70+ aid for high school exams and standardized tests. That's the one thing that computers/phones can't encroach on.