This benighted nation has an unenviable reputation: the most corrupt country in South America; the smuggling and counterfeiting capital of the continent; a state burdened by almost 200 years of dictatorship - a yoke only thrown off in 1989. Yet because Paraguay is so far off the beaten track, it is a good place to find the real spirit of South America. The typical small town in Paraguay is a montage of peeling paintwork, dusty streets and weatherworn faces with gently creased smiles. It feels like the Wild West but with no imminent danger of anything much happening.
This land-locked nation is a sleepy backwater where, it is said, some of the pale-skinned locals are descended from Nazi war criminals. It is a country of exiles. Graham Greene loved it. He lived and wrote at the Hotel Gran del Paraguay in Asuncion, a fading colonial relic which manages the undemanding achievement of having the best restaurant in Paraguay. Among the exiles are 10,000 Mennonites. The men wear black and the women are clothed from head to toe, their pale faces scorched pink by the harsh sun. Conversation is in the throaty burble of Platdeutsch (low German), and the local paper is named Aktuelle Rundschau.
Paraguay shares the same disadvantages - a shambolic capital, disparities of wealth, volatile politics - that afflict most South American nations. Sadly, it stops short of many of the more positive qualities. This landlocked nation lacks the beautiful beaches and beach-goers of Brazil, the Andes and the miraculous Machu Picchu in Peru. But what it can boast is a bit part in a dramatic piece of natural theatre.
When Bess Truman, wife of the American president Harry S Truman, saw the falls at Iguacu, she is said to have remarked, "poor Niagara". You can see why. There can be few waterfalls in the world more impressive or in a more spectacular setting. Almost two miles wide and 250 feet high, the falls cascade in two vast steps down from the southern Brazilian plateau into a deep gorge. All around is a sub-tropical rainforest rendered even more luxurious by the constant mist thrown up by the roaring water.
The Iguacu river forms the border between Brazil and Argentina and you can visit the falls from either country - indeed, you should see the view from both. The Argentinian side offers the better close-ups, the Brazilian side a better sense of the falls' grandeur - plus one unforgettable close encounter of its own. But for the full Latin American experience you should start your journey to this wonder of the natural world a few miles away, across the border in Paraguay.
Paraguay can be seen at its most vigorous, ramshackle and lawless in the eastern border town of Ciudad del Este, just a few miles from the falls. It is little more than one huge flea-market. Every day thousands of Brazilians cross the bridge over the River Parana in search of bargains. The town's streets are full of shops and stalls selling everything from top-of-the-range audio equipment to cheap T-shirts. We hadn't come to shop, but it didn't matter. The traders came to us. The first was a man with a vast tray on his head piled high with chipas, the savoury snacks incorporating eggs, cheese and manioc flour that Paraguayans eat on the move. But after him came the men selling counterfeit CDs, straw hats, colourful little FM radios, cheap footballs, toy helicopters, watches, and mobile phones.
When finally we burst free of this hustling, bustling hive of activity we crossed the bridge into Brazil - and found ourselves in a different world. Brazil is not a rich country, but tourism has made the city of Fos do Iguacu wealthy. It was like driving instantly from the third world into the first.
The streets of Fos were well-paved and clean, with neat road markings and no-one trying to jump the traffic lights. The people were well-dressed, the cars and the buildings were modern and spruce and the shops were smart. Unlike in Paraguay, there were rubbish bins on the street corners and neatly-planted green spaces. We could have been almost anywhere in the US or Western Europe.
Around the falls themselves the Brazilians have worked hard to preserve and protect the environment. The road to the falls has been closed - though, since this is Latin America, an exception is made for the rich if they have reserved rooms at the luxury Cataratas hotel overlooking the cascades. An open-topped double-decker bus runs every few minutes down to the falls, through part of the vast national forest on the Brazilian side of the river.
In here you will find, the guide books say, jaguar and puma, tapir, giant anteaters (an endangered species) and the raccoon-like coati. We saw none - though we did see any number of lizards, small, large and even larger. And there were birds flocking and swooping everywhere: parrots and parakeets, toucans and harpy eagles.
From the hotel you follow a pathway along the cliffs. The first sight of the falls is breathtaking enough, but as you walk on it just keeps getting better. The climax is a concrete walkway built right out into the middle of the falls at their deepest and most dramatic point, the Garganta del Diablo (the Devil's Throat). You stand deafened and drenched with spray from the top half of the cascade above you, watching the water rush over the lip of the lower half of the falls almost beneath your feet. I now know what the word "vertiginous" means.
The easiest access from the UK to the Iguacu Falls or Asuncion is on Varig (0870 120 3020; www.varig.co.uk) from Heathrow via Sao Paulo. However, the Foreign Office (0845 850 2829; www.fco.gov.uk) warns Varig is experiencing financial problems and cites reports from Brazil's civil aviation authority that, in April, 20 per cent of Varig's scheduled international flights and 31 per cent of domestic flights were cancelled.
Through the specialist company South American Experience (020-7976 5511; www.southamerican experience.com) you can get a fare for travel in July of £830 return to Iguacu (for Ciudad del Este), £860 return to Asuncion or £870 for an "open-jaw" ticket, flying out to one and back from the other. To combine the two: Ciudad del Este is around four hours' drive from Asuncion, or you can fly between them for around $100 (£55) one way.
To reduce the impact on the environment, you can buy an "offset" from Climate Care (01865 207 000; www.climatecare.org). The environmental cost of a return flight from London to Brazil is £20.60. The money funds sustainable energy and reforestation projects.
Hotel Paramanta, Avenida Aviadores del Chaco 3.198, Asuncion, Paraguay (00 595 21 607 053; www.paraguay-hotel.de): doubles start at US$86 (£51), including breakfast.
Hotel Austria, Ciudad del Este, Paraguay (00 595 61 504 213): doubles start at US$22 (£13), including breakfast.
Hotel Gran del Paraguay, De la Residenta y Padre Pucheau, Asuncion, Paraguay (00 595 21 200 051 53; www.granhotel.com.py): doubles start at 385 Argentine Pesos (£67), including breakfast.
Hotel Tropical Das Cataratas, Parque Nacional do Iguacu, Brazil (00 55 45 3521 7000; www.tropicalhotel.com.br): doubles start at US$178 (£105), including breakfast.
Iguacu Falls, Brazil (00 55 45 3521 4400; www.cataratasdoiguacu. com.br): the park opens daily 9am-5pm between April-September and until 6pm from October-March; admission R20 (£4.75).
Iguazu Falls, Argentina (www.iguazuargentina.com): the park opens daily 8am-6pm between April-September and 7.30am-6.30pm from October-March; admission 30 Argentine Pesos (£5.20).
Paraguay Tourism: 00 595 21 494 110; www.senatur.gov.py
Latin American Travel Association: 020-8715 2913; www.lata.org