The Museum of Man is a bit unusual insofar as it is an anthropological museum. So its exhibits are wide-ranging and usually very interesting -- delving into ancient and not-so-ancient civilizations and cultures. One exhibit I remember in particular was the gruesome one on torture devices. We saw it on a lark (for some reason we thought it would be amusing), but seeing all of the devices and reading the descriptions really made me ill and affected me profoundly. An ongoing permanent exhibit that I recall is "Footsteps Through Time" which shows you human evolution -- it isn't particularly compelling, I wish they would make it come to life a bit better. "Ancient Egypt" does a better job of this, although it could definitely use some more information about mummies!
I love their new concept of "Tower after Hours." Basically they adopt a country or culture for the evening, and bring it to life with food, drink, dance and music. I believe it takes place on Thursday nights, so you can treat it like a really hip, culturally aware happy hour.