Realistic time frame for GRE scores to appear in My GRE account
I believe, 3-4 years ago (woah...) when I took the test, it took approximately a month for the scores to appear. When you leave the test they will give you a score right there for the math and reading portions of the exam-- they state that these may change, but from what I've heard, and my own experience, they don't.

Things may have changed since I took it, however. Although, since human graders are still required for the writing portion, I doubt it.