One of the great natural wonders of the world, the Iguaçu Falls (Portuguese: Cataratas do Iguaçu, Spanish: Cataratas del Iguazú, Tupi: Y Ûasu "big water") are situated near the border of Brazil, Paraguay, and Argentina. The area is on the UNESCO World Heritage List.
Access to the Falls is usually done through one of the three cities in the so-called tri-border between Brazil, Argentina and Paraguay.
The city on the Brazilian side is Foz do Iguaçu - big and reasonably safe by Brazilian standards. The town on the Argentine side is called Puerto Iguazu and is small and pretty. Although the falls are between Brazil and Argentina only, Ciudad del Este, the city on the Paraguayan side, is just across the bridge from Brazil. It's a hectic (but exciting) centre for contraband and cheap electronic goods, and some say it's not safe there.
Border crossing between these countries is fairly relaxed - authorities assume most people are on a day trip across the border. US passport holders require a visa (US$130) to visit the Brazilian side of the falls which is NOT issued at the border. European Union passport holders do not normally need a visa to enter Brazil for tourism. Better check before setting off as the Brazilian side of the falls is "a must".
Beware that there may be lines on either side of the border, depending on the time of the day and holidays.
Also check regarding immunization requirements. Australian residents, for example, require yellow fever shots if returning to Australia within 6 days following a visit to Brazil. Brazil also requires yellow fever immunization prior to entering if your passport shows that you have visited some specific South American countries (Guyana, for example).
Both the Brazilian and Argentinean cities have nearby airports.
Foz do Iguaçu International Airport (Brazil) is served by TAM Airlines, Gol Transportes Aéreos, Trip Airlines, Sol Linhas Aéreas and LAN with direct scheduled flights to and from Lima, Peru, São Paulo Guarulhos/Congonhas, Rio de Janeiro, Curitiba, Recife, Salvador, Cascavel, Porto Alegre, Londrina, and some more. Pluna airlines from Uruguay has direct flights from Montevideo. The airport is located just off the main road between the city of Foz do Iguaçu and the entrance to the Iguaçu National Park. Taxis are readily available - go to the taxi desk at the entrance to the terminal building and tell them your destination (they speak English) and they will arrange for a car and give you a price. You can either pay by card at the desk or pay the driver in cash. Expect the fare to Foz do Iguaçu to be around R$25-30. The fare to the park entrance in Brazil is closer and will be less. The airport is on the bus route between Foz do Iguaçu and the National Park entrance. The bus service runs every half hour and is cheap (R$2.20), efficient and easy to use. The stop is right outside the terminal building - board the front of the bus and pay the person sat at the turnstile (change is given) before passing through. The bus passes many of the main hotels on the way into the city (stops are frequent) and ends up at the bus terminal on the far side of the city where there's a friendly tourist information office. In the other direction the bus will drop you off just outside the main visitor's centre at the entrance to the park.
If you arrive to Foz do Iguaçu airport and are staying at the Sheraton Iguazu (on the Argentinian side), or just staying in Puerto Iguazu city on the Argentinian side, it is recommended to rent a car at the airport instead (make reservations in advance), so that you can travel from the hotel to the nearby town (which you will want to do if you want to eat there and do some sightseeing) and also to give you the flexibility to go to the Brazilian side of the falls and visit Itaipu dam. Otherwise, a one-way taxi from Foz do Iguaçu airport to the Sheraton is R$100 (does not include AR$60/person entry fee for the park), and about AR$150 to go back to the airport from the hotel. A taxi from Foz do Iguazu International Airport (Brazil) to Puerto Iguazu (Argentina), will set you back U$S40. You will have to arrange to go to the Brazilian side of the park for about AR$150 or so by taxi (be sure to negotiate down). To go to and from Puerto Iguazu, there is a bus that costs AR$5 and runs every half hour but the last one leaves at 8pm so if you are dining later than that, you will need to hire a taxi for about AR$70. You can also rent a car from the hotel (they will bring the car to you) but book in advance (and check the rates) as there can be a shortage of cars and is usually more expensive (AR$300-450 per day).
If you arrive at Iguazu International Airport, there is a taxi stand at the baggage claim where you can book transfer to either Pte. Iguaze (if you're staying in town) or the Sheraton if you're staying there. Consider renting a car (Hertz, Budget, ...) instead to give you more flexibility, esp. if you plan to spend a day in Brazil as well. It's about 15 minutes from the airport to the park/ Sheraton and about 30-45 minutes to Pte Iguazu.
Buses from all major cities in the country arrive in each of the three towns (see there for details).
From Puerto Iguazu there are buses to the entrance of their side of the falls every half hour (currently at :10 and :40 past the hour for AR$15 return).
From Foz do Iguaçu buses run every half hour from the bus terminal to the visitor's centre at the national park entrance, passing many of the main hotels in the city along the way. The R$2.65 flat fare makes the bus a very cheap way to visit the falls and it's also easy to use. If you're starting your journey at the bus terminal you pay your fare on entering the terminal and board the bus through the rear door (the bus is No. 120 to 'Parque Nacional' - the tourist information office at the terminal will point you in the right direction if you have any trouble finding it). When boarding the bus anywhere else you use the front door and pay at the turnstile onboard. The journey takes about 40 minutes. Schedules can be found at the Foz do Iguaçu city web site, 
From Foz do Iguaçu to Puerto Iguazu: there is a bus that leaves from just outside the bus terminal, at the corner of Rua Mem de Sá and Rua Tarobá. It costs R$4 or AR$8. The bus may or may not stop at the Brazilian border checkpoint but typically will stop at the Argentine border checkpoint, where your passport will be stamped. You can also exchange foreign currency at the Argentine border checkpoint, but be aware that the bus may leave without you if you take too long, leaving you to take a taxi (approx. AR$80) or wait for the next bus. This bus terminates at the Puerto Iguazu bus station where you can catch the bus to the National Park.
From Puerto Iguazu to the Brazilian Iguaçu Falls National Park: take a public bus from the terminal (AR$10). The bus waits while everyone gets off at the Argentine Immigration for your exit stamp. It then drives onto the Brasilian immigration where it *wont* wait for you. No worries, get your Brasil entry stamp and then walk 150m to the main road. Heading right at the roundabout there is a bus stop to the falls, 10 minutes R$2.20/AR$7. (The town is to the left, 15 mins by bus). Conveniently there are large lockers that fit backpacks at the falls entrance (buy token in the shop - R$9). Which means you can see the falls and then take the bus back to town (or the airport) and get out. Too easy.
It is not uncommon for policemen to check passports in the Argentinian side of the falls, even during domestic journeys. It is advised to carry some documentation of citizenship. If you are coming from the Brazilian side, tell the bus driver you need to stop at the Brazilian border crossing to get your passport stamped. If you try to re-enter Brazil without having been stamped you may need to pay a substantial fine.
The main car rental companies have offices at the Brazilian Foz do Iguaçu airport. Make sure that you mention at the time of your reservation that you intend to cross into the Argentine side to visit the park. You need a special authorization from the rental car company for that. Insurance bought on the Brazilian rental car is not valid in Argentina. You need to buy a special "carta verde" while still on the Brazilian side. It is sold at lottery stands. A three-day pass costs R$45. If caught without a "carta verde" on the Argentine side you are liable to be charged very heavy fines.
Renting a car gives you a lot of flexibility in exploring both Brazilian and Argentinian side of the cataracts.
If you stay at either of the two hotels in the park (either on Argentinean or Brazilian side), you are within walking distance of the falls, so no need for taxis, buses etc. Consider this when planning your trip. See in "Stay" section for details.
Both sides of the park are well served with foot trails.
On the Argentine side of the park there's a small train leaving about every half an hour from near the entrance going all the way to the beginning of the trail to the Garganta del Diablo.
On the Brazilian side, there's a bus service connecting the falls with other activities. That service runs from the entrance to the end of the park every 10 minutes in both directions.
The Iguaçu Falls are an awesome sight as tonnes of water throw themselves over cliffs and the mist rises amongst the jungle. They are taller than Niagara Falls, and twice as wide, for which Eleanor Roosevelt is said to have exclaimed on her first sight of the Falls: "Poor Niagara!"
It is well worth spending a day on each side of the falls, especially if you plan to do any of the boat rides or other activities offered.
Don't just rush past the main viewpoints and leave. It's important to get a good perspective on the park overall to appreciate this awesome sight.
Whilst the majority of the falls are in Argentina, a better overview is had from the Brazilian side.
On the Argentine side (130 AR$ pp, second day for half price if you get your ticket stamped before leaving on the first day, subsequent days are free if you tell them you are staying at the Sheraton). Wear waterproofs and protect your camera as it can get quite wet on some viewpoints. Some people visit the waterfalls in swimsuits (recommended in summer). The park itself is fairly well organized, they have a train line so you can get from the entrance to the main circuits (Circuito Superior, Garganta del Diablo, etc. See bellow). They also have food stands inside the park close to the train stations, but food and drinks are very expensive there. It is a good idea to bring some food and water if you are going to spend the day on the park.
There are five main tracks all of which are paved and well marked with the exception of Sendero Macuco:
Circuito Superior - is a short walk to some nice viewpoints along the upper rim of the waterfalls
Circuito Inferior - is a longer walk on the bottom end of the falls with the main attraction being the lookout to watch Salto Bossetti and Dos Hermanas. This pathway leads also to the free ferry service to Isla San Martin (that may or not be closed), and the tour operators.
Isla San Martin - has two main lookouts to different sides of the falls. There are also a lot of birds. Access by boat only (free). This may be closed when the river level is high. You can always ask the park authorities or watch the information tv sets within the park to see if the access to the island is open.
Garganta del Diablo - The main attraction of the Argentine side. There is a free train running up to a 1 km-long walkway across the river to stand just back from the main horseshoe of falls where the roar and spray are most tremendous.
Sendero Macuco - is the trail through the rainforest to the Arrechea waterfall and is a good way to get away from the crowds. It's about 7 km return on an unpaved but easy path starting at the Estacion Central. Swimming is possible beneath the fall, so consider bringing a bathing suit and towel. An informative brochure for the trail is available from the park information desk. It is recommended to do it in daylight, so don't start it if it's 3 or 4PM.
Garganta del Diablo is the main attraction on the Argentine side - do not leave without having seen it.
On the Brazilian side (41 R$ pp, cheaper for Brazilian residents) you get an excellent overview of Devil's Throat and the rest of the falls, from both above and below.
Spectacular boat trips can be made under the falls.
If you go all the way to the "Las Cateratas" station, you will be offered e.g. wildwater rafting & abseiling activities at better rates. When you arrive shortly before the activities close for the day or they're just not busy you can easily bargain about the price and get a really good rate!
The Sheraton hotel right in the park provides a good alternative to the junk food stalls located throughout the park. There's a nice terrace you can rest from which you can see the mist coming out of the falls and also generally see toucans and other birds flying around.
There are some very good restaurants in the town of Puerto Iguassu, serving a very good choice of Argentinian wines.
On the Brazil side, there's a buffet that stands right next to the throat at the Porto Canoas station at the end of the walking trail. The food is not good but the view of the river makes for a surreal sight as you know the falls are really close by but you can't really see them other than the mist and the noise.It's a nice place to eat. In addition to the buffet at R$ 40 you can grab a (burger) combo meal at one of the outlets right in front of the buffet restaurant for around R$ 10.
Both on the Argentine and the Brazilian side of the falls there are enough opportunities to buy a drink.
There are only two options to stay inside the park within walking distance to the falls: Sheraton in Argentina and Hotel das Cataratas in Brazil. Both are a bit pricey and take advantage of their position. Some people prefer to stay in either Foz do Iguaçu on the Brazilian side or in Puerto Iguazu in Argentina, where a large number and range of accommodation options can be found. Transport to the falls during daytime is a 20 min bus ride.
Other than visiting the falls, the activities offered by tour operators on both sides of the park and having a drink/ dinner at either Pt. Iguazu or Foz de Iguazo there isn't much else to do in this area. So don't plan on staying your entire holiday here, 2 or max 3 days should do it. For the Brazil side you need no more than 4 hours total. Its often cheaper to fly out of the Brasilian side to Sao Paulo for example, than to take the bus (not to mention quicker).