These shows can always be found on the radio, no matter where you are, but their popularity seems to wax and wane. I know that Father Caughlin was one of the first big radio superstars, way back in the 1930s, and maybe you'd want to classify Walter Winchell as right wing as well, although I'd just say he was cynical. Most people will equate this term with more modern broadcast personalities such as Gary North, G. Gordon Liddy, and the Godfather of modern conservative radio, Rush Limbaugh.
Limbaugh's show became popular around 1990, when Republicans were becomming disappointed with the lack of effectiveness seen in the Bush administration as compared to his predecessor, Ronald Reagan. Bush was percieved as knuckling under to a liberal Congress, and starting an oil war in an attempt to compensate for his inadequacies. Unlike other talking heads, Limbaugh was the first conservative pundit to really lay into Bush for failing to fill Reagan's shoes, and he gave conservatives critical of Bush someone to listen to.
It didn't hurt that he used all sorts of tasteless gimmicks to fill out his shows. Early in his career, people who disagreed with him would get 'caller abortions', in which the phone would get cut off to the sound of a running vacuum cleaner. He would also court racist stereotypes in his characterizations of certain minority leaders. Specific examples elude me at this time.
Of course, the unwashed masses, feeling their needs unmet by the Bush administration, ate it all up. And when Bill Clinton won the election in 1992, Limbaugh's career really took off. At the peak of his power, Limbaugh claimed 20,000,000 people tuned in to his daily show, a number previously unheard-of in talk radio.
The power of these shows was based on the fact that they were so mindlessly opinionated that logic, fact checking and taste went right out the window. If you loved Rush, that was great. If you hated him, that was also great, because usually your complaints would end up sounding like the 'liberal whining' that was discussed on the shows. Groups like FAIR put together extensive lists of Limbaugh's inaccuracies (which can still be found on www.fair.org), but in this noder's opinion, they were missing the point, since they helped Rush use the common tactic of claiming that the rest of the news media has a liberal bias. (When asked if he believed in equal time for opposing views, Rush's response was "I am equal time!!").
The only way to hurt a host like Rush was to either not care what he said, or to remain calm and unmask him as a buffoon. In an appearance on the David Letterman show (one of his few appearances outside his own radio studio), Rush was asked by Letterman "Do you ever lie awake, late at night, and think 'God, I'm just full of hot air?'". As the audience roared with laughter, Limbaugh was speechless.
Limbaugh's popularity seemed to attract a criminal element to radio journalism: soon both G. Gordon Liddy and Oliver North had their own shows, both irrational in their own special ways; Liddy is famous for instructing his listeners to 'aim for the head' when the BATF comes through their door, and I myself caught North railing against the United States Constitution itself (namely, the concept of checks and balances) when a Federal Court judge overturned a school voucher plan.
How did intelligent conservatives take to this? Well, those pundits that didn't offer faint praise just kind of ignored these people, and tried to treat the phenomenon in the same way that, say, Maya Angelou might treat Oprah Winfrey; as somewhat dim and embarassing populists that might lead a few people to read their books.
The talk show fad hit its turning point, or more accurately, its downfall, with the Oklahoma City Bombing in 1995. When it was discovered that right wing extremists were the people behind the attack, many of the chickens set flight by Limbaugh, et al, came home to roost. Suddenly, the whining done by Democrats that Limbaugh, Liddy, and North were just mean-spirited and destructive seemed a lot less trivial. Since that date, the number of listners has steadily declined, and today, almost no one takes these people seriously. Time will tell if we see a resurgence of the popularity of these talk shows in future decades.