Even I Love Lucy has elements to it that simply will not work now. Of course, the show is a timeless classic and always will be, but... the elements of "men are the earners and women are the spenders," women can cheer themselves up just by buying a new hat, and it's the role of the husband to discipline the wife have gone completely out the window sixty years later.
Yep, sitcoms have done a complete 180 in that realm. Now it's the husbands that are the "children." Everybody Loves Raymond, King of Queens, Yes Dear, etc. all portray men as dumb, childish, unreliable, and incompetent. This also shows up often in commercials. And it drives me crazy! It sends the wrong message to young men. It sends a subconscious message to them that this is how they're supposed to act. Which is why I'm thankful for people like Brett McKay at artofmanliness.com who are trying to help men find their true manliness (and not the comical way portrayed in the media).
I think any mildly-popular-today-but-forgotten-tomorrow show like "Broke Girls" won't age well. As will any show that, as Applesuace pointed out, relies heavily on topical humor like SNL, the Simpsons, South Park, and all of Seth McFarlane's shows. A perfect example of this is "In Living Color." For those who are too young to remember (or to have even seen it), "In Living Color" was basically Fox's answer to SNL in the early 90s. It was pretty funny and cutting-edge at the time, but if you watch it today, WOW! Most of it has not aged well.