Back yards are an interesting phenomenon. Most people, even confirmed city-dwellers like myself, see their appeal. Certainly the thing I miss most about my previous DC rowhouse was that it, unlike my current one, had a yard that while very small was definitely big enough to pass some time in and even cultivate some vegetables. But at the same time, in practice people don't utilize lawn space for a very high proportion of the time -- considering how often you're either not at home, or asleep, or watching television and the like the yard is most often standing unoccupied.
Jonathan Zasloff observes that shared yard space (as in according to him a show for kids called Backyardigans or else perhaps Big Love) where several separate single-family homes would converge on a single back yard might be appealing to some people. But of course like a lot of things that might increase residential density with the various positive impacts on affordable housing, transit accessibility, climate, public health, etc. that entails it's generally illegal to build this way.
Photo by Flickr user D'Arcy Norman used under a Creative Commons license
Matthew Yglesias is a former writer and editor at The Atlantic.