We know that Panem exists in a post-apocalyptic North America but are there other established governments on other continents?
None that we know of. Panem is, as far as anyone else in the story knows, the last human civilization on Earth. The events preceding the creation of Panem (a combination of natural disasters and man-made war and disease), some 200 years ago, have rendered most of the rest of the world, including most of North America itself, uninhabitable, and dangerously depleted the world's population.
Now, from a purely realistic perspective, it seems unlikely that Panem's people are the only humans left on Earth. There are plenty of people living in plenty of places that would neither be very susceptible to a major natural disaster, nor worth the effort of deploying a WMD. So, there is every chance of the other major landmasses (Africa, Eurasia, South America and Australia) harbouring some remaining human populations, probably mainly nomads moving from place to place hunting what animals are left.
However, those countries and their people are few and far between. Mongolia, for instance, is not real high on anyone's target list, but it has the bad fortune of being landlocked in between two of the world's foremost military and nuclear powers. Similarly, the Himalayan nations are no real threat to anyone, but lie in the middle of a trifecta of conflict (China, India, Pakistan). Pretty much every nation in Europe, South and Central America, the Middle East, and Africa are on SOMEONE's hit list. Australia is too close to Western power factions to escape unscathed, and the most habitable areas are the ones with the major cities (and close to the ocean, meaning a rise in sea levels would submerge a large part of the habitable land).
North America is of course on many hit lists; the primary reason any of it would survive is probably due to the United States having invested relatively early in a missile defence system. That at least prevents or reduces the nuclear attacks from sovereign nations. We'd still be subject to global warming, epidemic, and terrorist attack rendering large swaths of the most densely-populated areas inhospitable. What's left are small tracts of land in between what used to be dense population centres, that have some remaining economic value: farming (11), ranching (10), fishing (4), mining (12 & 2), textiles (8), lumber (7), and what's left of the tech and consumer goods industries (1,3,9).
But, the basic idea is that while the Capitol has advanced technology significantly in many areas, in others they are woefully limited compared to today. For instance, they have "hovercraft", the exact nature of which is not detailed in the books but is probably based on ducted-fan propulsion much like the craft in Avatar. These craft are short-to-medium range, probably using a battery charged at the home base. Fossil fuels of many kinds are in such short supply that air planes as we know them today are infeasible (though not unknown to the more educated people of Panem). So too are large ocean ships. So, trans-oceanic travel is generally considered impossible by Panem's residents (none of which would have any knowledge of sailing ships), and thus even if people were still scraping out a living elsewhere on the planet, Panem has neither the will nor the resources to go find out.
We must consider, that the novels were consequently written from Katniss' point of view. The form reminds of a so-called writing therapy, used by psychologists to help people, who try to overcome mental problems. We do not even learn, how and why she begun to write down her memories. Perhaps she did it as the result of someone's advice - Peeta may have given it to her - or it was her own idea, following Peeta's example, when he tried to get rid of his nightmares by artistic work.
So the books (here I avoid the term "novels") can be seen as some kind of very personal and private memoirs, not as some kind of historical documentary. It is the author's special merit, that she continued this form through the trilogy without following the temptation to add some kind of timeline. So the readers experience Katniss' own horrors as well as her own knowledge about the world, where she must live.
Katniss has attended the school in District 12, but what did she learn in an educational system of a dictatorship? What could she learn? Panem reminds me of modern North Korea: Pyongyang as the Capitol and the rural provinces as the Districts. What are children taught in North Korean schools? The answer: total loyalty to the party and the "beloved leader" as well as those skills, which are necessary to become a productive subject of this state. What do these children know about the rest of the world? Just that the people there are living in total poverty, oppressed by evil capitalists.
What did the children learn in the school of District 12? Surely how to read and to write as well as some other basics, which are necessary in every society with some technology - after all, even in the 18th and early 19th century mining needed a high level of technical sciences. The first steam engines in Europe were built to get water out of the mines. But what else did the children of District 12 learn, especially about history? Can the Capitol risk to allow the schools of the Districts to teach them about the American Revolution of 1776, the life of Abraham Lincoln or the civil rights-movements around 1965? No dictatorship would do that, because these examples show, that a nation can overcome any resistance, when the people want changes and reforms.
So it must be doubted, that Katniss has learned much about the real history of North America as well as the situation outside the borders of Panem. It is also doubtful, that those facts, which she was taught, were correct. After her father's death she lacked the time to study any longer, because she had to take care for her family. In the years after the end of the trilogy Katniss were forced to overcome her own demons, supported the rebuilding of District 12, married Peeta, became a mother and took care for two children -surely she had not much time to improve her education, even with her husband's help.
Even in the free society of a democratic nation the historical knowledge of the people can be incomplete, because the schools concentrate on the national history. An example will show that: in Britain even the youngest school-kid is able to tell the whole biography of the Duke of Wellington, including his campaigns in India and Spain, the Battle of Waterloo as well as his political career as a minister and finally as prime minster of the United Kingdom. But in the history books used in Germany the Iron Duke and the British army suddenly appear at Waterloo, without any explanation, what the British nation did since Trafalgar. Obviously they were just drinking beer peacefully in their home-country's pubs, while the gentlemen played whist in their clubs.
For these reasons we can not be sure, whether Katniss' knowledge about Panem's history are correct. It is perfectly possible, that she just quotes those facts, which were taught to her in school, without any attempt to check them. The wars and disasters may be a nuclear world war and the effects of global warming, but also a series of internal conflicts, that caused the old USA to disintegrate similar to the former Yugoslavia, an eruption of the super volcano under the Yellowstone Park and the feared earthquake, which may one day destroy California. A combination of these possibilities will surely cause even the end of the United States.
So nearly every situation is possible outside of Panem. A world, destroyed by a world war and global disasters with some remaining pockets of the old civilization (or perhaps barbaric fiefdoms), may wait for brave travellers, but also free nations with modern societies and a superior technology, including space travel and colonies on other planets. Something seems to be there, because Katniss mentions, that Gale got a job in the military - and why should the new republic keep armed forces, if they do not expect the necessity to need them?
Of course the question must be asked, why other nations did not intervene, when the Hunger Games begun. First of all, after some global disaster even technologically advanced societies may have been busy to rebuild their countries, and so they had no possibilities to stop the games. Besides Panem can still be considered an independent state - and even if the other nations despise it, an intervention may be complicated as long as it does not threaten its neighbors - like Canada, Mexico or the Caribbean - or the world peace. The world may impose sanctions like a total blockade, but as long as the Capitol can exploit the Districts, this may not harass the rulers.
Furthermore any direct intervention demands a military campaign on a global scale by transporting the armed forces from Europe, Australia or Japan to North America. World War II has shown the logistical troubles of this kind of warfare. Would any nation risk the lives of its soldiers just to rescue some children in a destroyed country, that has no longer any importance? For the governments this will be a really tough choice. Besides the Capitol threatened to use nuclear weapons against the rebelling Districts. We do not learn, whether they really had any capability of mass destruction left - it could have been a bluff. But could the other nations be sure about that?
In the end all these reflections must be speculative, as long as the author has not published some kind of official compendium including a history of Panem. But if we take the trilogy as Katniss' attempt to overcome her personal demons hidden in her mind, then anything is possible, including a return of Panem into a civilized world. Perhaps one day the author will continue the story: let us imagine, how Katniss and Peeta leave Panem to visit Europe, where they are hailed as the heroes of the Mockingjay-revolution ...
My guess is that after World War 3, the world was divided. Some parts became uninhabited while others became more densely populated. Due to WWIII, the human race was majorly depleted and survivors grouped into places that were safe, creating nations like Panem. However very few nations knew of other nations' existence and Snow created a unbreakable barrier around Panem. Therefore the Hunger Games were unnoticed by any other nations.
In Chapter Two of Mockingjay it is strongly implied that Panem is the last bastion of humanity in the world:
"Oh, I'm not too upset to answer that." Peeta takes a deep breath and then looks straight into the camera. "I want everyone watching--whether you're on the Capitol or the rebel side--to stop for just a moment and think about what this war could mean. For human beings. We almost went extinct fighting one another before. Now our numbers are even fewer. Our conditions more tenuous. Is this really what we want to do? Kill ourselves off completely? In the hopes that--what? Some decent species will inherit the smoking remains of the earth?"
This is reiterated in Chapter Six of Mockingjay:
"It's not that simple," he shoots back. "We were in no position to launch a counterattack until recently. We could barely stay alive. After we'd overthrown and executed the Capitol's people, only a handful of us even knew how to pilot. We could've nuked them with missiles, yes. But there's always the larger question: If we engage in that type of war with the Capitol, would there be any human life left?"
If there are no humans elsewhere then there are presumably no governments either.
In Chapter Fifteen of Catching Fire Katniss sort of implies that there is other civilization beyond Panem:
I can't argue that Finnick isn't one of the most stunning, sensuous people on the planet.
Notice that she doesn't say "in Panem". This would imply that there are other people elsewhere on the planet and Finnick is even more sensuous than them. If there are any significant amounts of people on other continents, there would likely be some form of governments controlling them.