In 1962, the "father of cryonics," Robert Ettinger predicted that the bard's popularity with the reading and theatre-going public would inevitably wane. The prediction also appeared in the April 1967 issue of The Futurist magazine, where it's explained that people of tomorrow won't care for Shakespeare's "weak intellect."
But Ettinger insists that the biggest reason for the demise of Shakespeare will be that people in a couple hundred years won't even recognize such base things as greed, lust or ambition. Echoing the techno-utopian sentiments of his generation, Ettinger believed that Shakespeare's days were numbered because "virtually unlimited resources" will give future humans an entirely new outlook on life — and in turn, on the arts.
From The Futurist:
In a few hundred years, Ettinger maintains, Shakespeare "will interest us no more than the grunting of swine in a wallow. Not only will his work be far too weak in intellect and written in too vague and puny a language, but the problems which concerned him will be, in the main, no more than historical curiosities. Neither greed, nor lust, nor ambition will in that society have any recognizable similarity to the qualities we know. With the virtually unlimited resources of that era, all ordinary wants will be readily satisfied, either by supplying them or by removing them in the mind of the individual."
It's obviously too early to call Ettinger's prediction right or wrong, but allow me to go out on a limb with my own prediction: in a hundred years, everyone reading this post will be dead. And whether we've achieved some semblance of a post-scarcity society or Earth is little more than a pale blue Waterworld-esque dystopia of mutant polar bears, themes of greed and lust and ambition (and thus, Shakespeare) will still resonate with humanity.

Image: Actual photograph of Bill Shakespeare taken by Kelsey Campbell-Dollaghan at Gawker Headquarters, International