The Radio Dies First

A two-way radio is put out of commission to allow the plot to proceed.

Back before Can You Hear Me Now?, the device that could really put a crimp in a plot's need to keep the characters isolated and cut off from information was the two-way radio. So in a lot of Twentieth Century media, the radio was put out of commission as quickly as possible. There were three main ways of doing this.

Vehicle crash. Whenever a plane or boat had to make a forced landing, the radio always, always broke, no matter how gentle the landing seemed otherwise. This was close to Truth in Television before the widespread use of transistors and printed circuits; radios used a lot of easily breakable tubes, and wires jarred loose with relatively little provocation.
Interference. This was usually accomplished with the use of heavy weather conditions, which also helped isolate the characters. Imaginative writers could use interference to give only partial information to the protagonists, which they can then totally misinterpret.
Sabotage. This ranges from the subtle (breaking or stealing a single hidden tube) to the blatant (taking an axe to the radio set.) This is usually a big hint to the protagonists that what's going on is no accident or series of coincidences.

Many stories in the appropriate time period will have a radioman usually named "Sparks" who will be stuck trying to repair the radio or get through the interference for most of the story. His isolation often causes him to score badly on the Sorting Algorithm of Mortality.

In more modern stories, this has been replaced by The Cell Phone Dies First.

Examples of The Radio Dies First include:

Comic Book

An issue of The Maze Agency uses the sabotage variant, smashing the radio and then blowing up the boat to strand the characters on an isolated island.

Film

In Crimson Tide, the loss of both the boat's radio and longwave buoy (partway through a transmission) left the crew unsure whether an order to launch nuclear missiles had been countermanded. The tense scenario comes complete with an engineer racing against time to repair the radio.
Similarly, the failure of a strategic bomber's radio meant that the failsafe in Fail Safe did not, well, fail safe.
Similar to Fail Safe, the bomber's radio is damaged in Dr. Strangelove, meaning it can't be recalled.
In The Wicker Man, the natives sabotage the policeman's plane, cutting out his communication with the mainland.
Fantastic Voyage: It's the vital laser that is sabotaged, and the only source for parts to fix it is the radio.
When the shark starts its climactic attack in Jaws and Chief Brody tries to call for help, Quint destroys the radio in a fit mad obsession to catch it.
Done in Tremors 2. The creatures destroy the radio accidentally because they associate heat with prey.

Literature

In The Heights of Zervos by Colin Forbes, a British saboteur disguised as a Nazi takes advantage of a sniper attack on "his" unit to put a bullet through the radio.
In the second book in The Mysterious Benedict Society series, The Mysterious Benedict Society and the Perilous Journey, Reynie Muldoon (the main protagonist) actually pitched the radio out of a train because he mistakenly did not consider the person on the other end to be trustworthy.
In The Shining, one of the Overlook's first overt hallucinations is that of Jack's dead (and abusive) father, berating him over the radio that's the only link back to the mainland. It keeps it up until Jack snaps and smashes the radio.
In The Beacon To Elsewhere by James H. Schmitz, the protagonist has two communicators, and the same incident stops him using either of them. He's in an area where something is interfering with the planet's power grid; the power failure brings down his flying car. One of his communicators also runs off the grid, so it can't be used. The other has its own power source, but gets destroyed in the crash.
Magic interferes with tech in the Dresden Files, and cell phones (and radios and other relatively fragile/complicated electrical systems) are the first to go, likened to canaries in mines.

Live Action TV

On Lost a large part of the pilot is spent trying to get the plane's radio working so they can call for help. A few months later they find out that all radio signals from the island are jammed on Ben's orders. Anyway the weird nature of the islands makes communication with the outside world very tricky.
When the castaways are stranded on Gilligan's Island their radio transmitter is broken but they can still receive radio signals including a report of how the search for their boat is called off.
The Doctor Who serial "The Power of the Daleks" uses the sabotage version when the Doctor discovers that the communications room of the Vulcan colony has been destroyed.

Video Game

Half-Life 2's extremely finicky video communicators.
- Also, one of the reasons why Gordon has to go from help in the first game is that the resonance cascade took out the phones.
A mission in Vietcong pretty much carries on due to the radio not reaching a VC underground tunnel.

Real Life

An Australian air pioneer crashed in the outback and was unable to signal for help because the plane's transmitter was powered by a dynamo hooked directly to the engine.
The Mann Gulch fire of 1949 that killed 13 smokejumpers. One of the things that went wrong was that the parachute dropping the team's radio failed to open, smashing the radio. It meant they were out of contact and could not get back-up or call in aid for their wounded members.