Harvard University doesn't officially recognize fraternities and sororities, so any organizations on its campus does not get funding or a house, etc. However, there are three sororities (if I remember corrently, they are Kappa Alpha Theta, Delta Gamma, and Kappa Kappa Gamma). They function pretty much the same as any sorority anywhere else; all recruitment, parties, etc. are done in the dorms or on other common areas on campus. I also know some Harvard girls who participate in city-wide sororities, like our Boston chapter of Alpha Kappa Alpha or the community-based sorority Delta Psi Sigma.
Greek life at MIT is surprisingly huge for a technology-heavy and northern school. We have 6 sororities and 26 (last I checked) fraternities. According to statistics, about 50% of men and 40% of women will pledge a GLO during their time here. We only have NIC/NPC organizations here, along with a service fraternity (APO) and a professional fraternity (AKPsi). There are no Christian, music, or MCGO's... nor do I ever recall an interest being present for any of them. I think most of our frats/sororities are diverse enough to begin with. Everyone is super loyal to their GLO, and while we don't host a ton of Greek events (think Cyprus-Rhodes Greek life), we do have many opportunities to show our support. Most of the GLOs on campus, in fact, are known for two things: 1) their parties, and 2) their annual philanthropic events. I definitely know that the sororities (aside from very blatant stereotypes that are tossed around) are best known for their annual events - AXO has Lipsync; APhi has the King of Hearts male beauty pageant; AEPhi has their Spaghetti Dinner; Theta has their KATwalk fashion show (clever); Sigma Kappa (which is NEVER called SigKap up here) has Late Night; and Pi Phi has their Pie Sale and Read-a-thon. As for frats, they are mainly known for their parties
There are definitely a lot of trends and "stereotypes" within each GLO, but I think that everyone accepts that and ignores it.