If we attempt to look into the future, I think we see that computers are likely to permeate every aspect of our culture. If they continue to decrease in size as they have been doing, they may actually end up being embedded in much of the stuff we use.
We should also notice that programming itself has a huge gradient in terms of difficulty. Things like Scratch, and other block programming languages make the act of programming easier, where amateur developers can focus more time on trying to solve the problems they are working on, and less time figuring out which parenthesis they missed.
So we have two trends - that programming is becoming easier to do, and that computers are becoming more common. Both of these lead me to the conclusion that not being able to program will eventually be akin to being illiterate. You won't be able to use and modify many of the tools of the future without some programming skill.
Further, many people are developing some of the core programming skills in pieces. Look at http://ifttt.com/ for example. This is an example of using apps as procedure calls, and writing very short subroutines to handle tasks for you. It is a perfect example of how programming is beginning to permeate popular culture.
Soon, telling people not to learn how to program will be much like telling people not to write or not to do math - it will be a bit ridiculous. We will just need to be able to use better systems for keeping track of who is an amateur, and who is a professional, much like we do with writing and mathematics.