A lot of Pulp Fiction (1994) depended on the characters having cell phones.
The first MicroTac came out in 1989 (and cost between $2,495 and $3,495.) By 1991 the older models were being sold for the aforementioned $0.01 each. When I got mine, people were waiting in a line across the Best Buy store to get them.
Oy, such a deal! 
The episode of The Sopranos where Paulie and Christopher were lost in the woods depended heavily on cell phone use too.
This is the only answer. They had an entire display mechanic for phones and like 80% of the cliff hangers had 2 or 3 characters in each quadrant waiting pensively for a phone call or hearing horrible news.
Lots of phone activity in Breaking Bad. People are saved by last minute phone calls, people die because of unanswered phone calls, phone calls are make while careening through traffic, multiple burner phones get broken in half, phones are hidden in toilet tanks, a fake phone call foils a DEA agent…etc.
That’s my favorite episode.
Was there an episode of Green Acres that didn’t at some point have someone (usually Oliver) climbing that pole to make a phone call? And how many episodes were about him trying to get better phone service? There was at least one episode that centered around him trying, unsuccessfully, to get the phone moved into the house.
And the phone technology was primitive for the time. We had a non-partyline dial phone at that point.
Maybe I’m wrong. Did the rural south really not have dial phones in the 60s?
The Jerry Lewis MDA Telethon.
When Leverage was on, resident hacker Alec Hardisson had ridiculously over-the-top “hack a Government facility with my phone” powers.
IT Crowd
“Hello, IT, have you tried turning it off and on again?”
Depends a lot on where you were.
People who grew up in metro areas, served by Ma Bell, sometimes think the whole country was wired the same way they were. But small towns and rural areas had often only gotten telephone service due to the New Deal–era Rural Electrification Administration establishing co-op phone companies, in some areas not until the 1950s. Other small cities had independent telcos with little investment capital to work with. A few sparsely populated parts of the Intermountain West didn’t get phones until the cell phone was invented; it just cost too much to string a wire 40 miles for one or two subscribers.
Even in places that had some kind of phone company, the equipment might date from the 1910s—before subscriber dialing. The exchange might be some oddball or homegrown deal whose only connection to the national network was a trunk line or two run from a nearby big city.
So yes, it’s absolutely possible that phone service in Hooterville was that primitive.
My post that you responded to was in reference to Andy Griffith not Green Acres (Hooterville), but I suppose your answer might also be applicable to Green Acres, although Oliver’s main problem was having to climb a phone pole to use the phone and I’m pretty sure that was never a real issue anywhere.