The availability of GRE scores depends on whether paper or computer format is used. With the paper-delivered exam, scores are accessible from a student's "My GRE Account" about six weeks after the test was taken. Results of the computer-delivered test are online in 10 to 15 days.
People who have taken the computerized test are able to obtain unofficial scores for the verbal reasoning and quantitative reasoning sections at the testing center right after the exam. However, results of the analytical writing component are not available then.
The GRE website lists approximate results dates for each date the exam is offered.