Star Trek TOS had computers galore. Tricorders, medical bays, the ships main talking computer, I'd argue all those screens and buttons and that thingy Spock looked into were all computers. Not to mention all the computer antagonists and various backdrop pieces.
They also had cell phones.
But go back and watch some of the episodes; it's still thin compared to the reality of today, let alone the reality of the future. Communicators that are like cell phones, sure, except that they only do voice transmission. My real-life cell phone is more powerful than my first couple of computers and has the apps to boot... and I have a piece of crap generic cheap cell phone, not even an iPhone. Talking computers that get asked very simple questions and are "working" for several loud seconds. No computer graphical enhancement of anything on the viewscreen (until the movies). Mainframes that generally need to be walked up to and used. The feel of the tech is very different.
Please understand I'm not complaining. This is one place where Star Trek has a legitimate claim to being ahead of the curve (although they pretty much jammed in that one spot and are now way behind) and I tend to be down on Star Trek at this point as my parenthetical shows; my point is that even so, the computers aren't as well integrated into people's lives as they are even today. Obviously, in the 1960s the special effects technology wouldn't have been there even if a time traveler from the real-life 21st century came back and tried to do it right with local tech and on a budget.
(And I don't mean to imply that's the endpoint of electronic development either, it's just something I can definitively say that the future, that is, "now", definitively already possesses.)
Now hard sci-fi faces the other side, which is that there's no evidence that it's going to stop before completely rewriting the universe as we know it (see endtime's link to Accelerando).
Asimov lived long enough to ret-con a sort of explanation in, as I understand it ("Robots suppressed computers!", although that still preserves the weird way in which robots were invented long before computers in his universe which makes no sense at all), but the lack of computers is still shot through his fiction and all fiction of that era, with just a few fragmentary exceptions here and there.