Although it was probably said earlier, the first time I recall hearing it was around 1980. It was "I doubt 2 years from now people will be using email." at that time. Maybe it wasn't exactly 2 years, but it was much less than 20.
Then it's soon the late 1980s, and we're still using some form of email. We hear, "I doubt 5 years from now people will be using email."
Quickly enough, we're in the early 2000s. Hotmail has really taken off, Yahoo! Mail is pretty popular, too, and Gmail will be coming along very soon. Nevertheless, people are saying, "I doubt 10 years for now people will be using email."
Here we are, about a decade later. Guess what? We're still using email, and more than ever. And what do I read today? "I doubt 20 years from now people will be using email."
I'm quite confident that when we're in the 2030s, we'll still be using email.