This makes sense not only from an environmental viewpoint, but also because so many of the materials in old buildings are much better quality than new materials. Old 2 x 4's, for example, are not only thicker than new ones from Home Depot, they're usually sawn from old growth timber that has a much tighter grain and is therefore stronger than newer wood.
What we particularly like about the ReBuilding Center is their commitment to deal with issues of social justice... having a house deconstructed does take more labor than just knocking it down and sending the whole thing to the dump, but it makes more sense to spend money on workers earning a living wage than on dump fees.
And that's not just an abstract, wishy-washy equation: when the ReBuilding Center went to New Orleans to help clean up after Katrina, the $6000-$10000 it cost to deconstruct damaged houses was about what the government paid contractors to just send them to the dump.