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Actually, I think "Life After People" is not so much inspired by "I Am Legend" as it is by the wonderful book _The World Without Us_, which was profiled here on Salon at its publication.
I've always thought, though, that television runs on memes (obviously). For a while, it was all about vampires -- Buffy, Angel, movies, and tons of History/Travel/Discovery Channel "documentaries." Then it was all ghosts, all the time. Lately, appallingly considering that it happened after 9/11, there's been a spate of mega-disaster shows. Hell, even the Weather Channel got into the act. What is Yellowstone became a megavolcano again? What if an F5 tornado hit Dallas? What if San Francisco has another great quake?
Now the meme is "global human extinction." Don't worry, it'll be Nostradamus again soon enough.