At Brown, we face a set of problems which are different from those of state schools, and even different from some of the other schools in the athletic league. For one, our campus is extremely left-leaning (but so am I, so it's not a problem) and therefore anti-Greek. I was a dorm counselor this past year, and my first-years had no problem (from the first day, no less!) about how they felt Greeks were elitist, how we stereotype, blah blah blah.
With that in mind, Greek life is here to stay. We have 2 NPC sororities (AXO and Theta), 4 NIC fraternities (AEPi, Theta Delta Chi, Sigma Chi, and Phi Kappa Psi), 3 local fraternities (Delta Tau, Chi Kappa Sigma, and Delta Phi), 3 national coeds (Alpha Delta Phi, St. Anthony's Hall/Delta Psi, and Zeta Delta Xi). The 3 coeds refer to themselves as "literary societies" and attract an eclectic bunch. Rush is in late January/early February. We are all residential, meaning that all of our houses are on-campus dormitories, in the same quadrangle. The non-residential Greeks include representatives of the "Divine Nine" of the NPHC and the Latino/a Greek groups. Many are members of city-wide chapters, and some groups often allow membership for RISD students (last that I had heard). As far as I know, we don't have Alpha Phi Omega, or it's inactive. We used to have DU (like, in the '60s), but they tore down their house to build an obscenely ugly library.
The Greek system at Brown, despite its vitality, gets a lot of criticism for being a bastion of white privelege (and, uhhh...the Ivy League isn't a bastion of white privelege?) and being elitist.
There hasn't been any talk of disbanding it, I think everyone realizes that our most famous alumni are Greek (Ted Turner, JFK Jr., the Nantucket Nectars guys, Raymond Hood), and Greeks are some of the largest benefactors.
At Harvard, greeks are allowed to band, it's just not school-sanctioned.