Half joke: If I had to bet, I would guess that reading will exist for as long as civilization does.

More seriously: I am less certain that it will exist in its current form (mass media, publishing houses, etc), but I am certain that textual information will be a standard means of communication and that people will read it. I do think that computer-assisted cognition (including computer-assisted reading) are eventualities at this point. This sort of thing fundamentally challenges the concept of reading: is your brain (by computer-assistance) scanning a hard drive reading? Even though it's alien to us now, I think the answer is yes.