Top business schools accept exam scores administered by two different agencies. Each agency has its own exam. The two most popular exams are the GMAT and GRE.
In the past, top MBA programs predominantly used the GMAT exam. The GMAT is generally considered more difficult especially because of its Data Sufficiency quant section that asks candidates whether there is enough information to answer the question rather than to actually answer it.
But business schools are businesses, too. They want to attract as many applications as possible. Of course the number of spots they have available is limited. The lower their acceptance rate is, the more prestigious their school will be perceived to be. So in an effort to increase the number of applicants and encourage applicants from all kinds of disciplines to apply, top MBA programsdecided to accept applications from candidates who actually were not originally thinking about business school. The applicants who take the GRE actually think about going to graduate school to get a master's degree in psychology, music, education, and other fields.
The business schools figured that if they could tell all these GRE applicants to just fill out a few extra forms and apply to their schools, then the business schools could not only diversify their candidate pool and class demographics, they could also reduce the percentage of admitted candidates. All of this bodes well for the business schools as admissions get tougher and tougher and the perceived prestige level of their school gets higher and higher.
But for many years no one did it. No business schools adopted the GRE. But once a few schools decided to accept the GRE, the rest of the top bschools had no choice but to accept it as well. After all, if you are a top MBA program and your competitors are accepting more candidates, lowering their admission rates and getting perceived as more prestigious, why wouldn't you lower yours as well?
So it becomes a snowball effect where one guy starts the trend and everybody else follows. These days most top schools accept GRE scores.
Still, as an applicant, if your intention is to go to business school and your background track record shows, that you really should take the GMAT exam as it is still considered as more rigorous. The GRE could be perceived as an easy way out.
On the other hand, if you did indeed study psychology in college and want to pursue a master's degree, but also wouldn't mind applying for an MBA while you're at it, then take the GRE. Use it to apply to your graduate program and also use it to apply for the MBA and see what happens. After all, business school admissions is all about diversity so if you're on the graduate route, you may have a better chance than you think.