I seem to remember an episode of a show back in the 80s that dealt with this. It may have been the New Twilight Zone or something similar. The episode revolved around one guy in a society that was constantly connected by way of phone, fax, beeper, and a few other things (but I don't think e-mail was one - this was the 80s!). The guy wanted to get some peace and not be constantly (and I do mean constantly!) within contact. When his family, friends, and coworkers couldn't get in touch with him (he kept destroying all the gadgets), they became concerned, and thought he was crazy for wanting to be alone sometimes. I think he ended up getting committed at the end of the episode.
I've been thinking of this particular episode a lot recently, because it seems that the society that was shown has actually come into being!![]()
That sounds like a Ray Bradbury story - titled "The Assassin" maybe? Yes, it's definitely all come true.