The Amazon River is the worlds greatest river. The Nile River of Africa may be slightly longer than the Amazon, depending on the channels measured, but for many other reasons the Amazon River is the undisputed greatest river on the planet, in solar system, and perhaps even in the entire galaxy (we won't try and make a claim for the entire universe!).
If size is important to you... The average discharge of water into the Atlantic Ocean by the Amazon River is approximately 175,000 M3 per second, or between 1/5th and 1/6th of the total discharge into the oceans of all of the worlds rivers!!! This discharge is 4-5 times that of the Congo River, and 10 times that of the Mississippi River.
The Rio Negro, a tributary of the Amazon, is the second largest river in the world in terms of water discharge, and is 100 meters (over 300 feet) deep and 14 kilometers (~9 miles) wide near its mouth at Manaus, Brazil.
Raindrops keep falling on my head! Average rainfall across the whole Amazon basin is approximately 2300 mm (or ~7.5') annually. In some areas of the northwest portion of the Amazon basin, yearly rainfall can exceed 6000 mm (almost 20')!
Where does all that water go? All of the water that is discharged into the Atlantic Ocean is actually only about 1/3rd of the water that falls into the Amazon basin as rain. Where does the other 2/3rds go? Up to half of the rainfall in some areas may never reach the ground, being intercepted by the forest and re-evaporated into the atmosphere. Additional evaporation occurs from ground and river surfaces, or is released into the atmosphere by evapo-transpiration from plant leaves. All of this evaporated moisture re-enters the water cycling system of the Amazon, and a given molecule of water may be "re-cycled" many times between the time that it leaves the surface of the Atlantic Ocean and is carried by the prevailing westerly winds into the Amazon basin, to the time that it is carried back to the ocean by the Amazon River.
A long and winding river road. The total length of the Amazon River from its source springs in the Andes (taking the Ucayali River as the continuation of the main river into the Andes), is estimated at 6518 km (not including all river bends, and measured the short distance around Marajó Island in the mouth of the Amazon), or ~4075 miles in length. This is exceeded only by the Nile River (including the Kagera River) of Africa with a total length of 6671 km (4170 miles). The headwaters are located high in the Andes at an elevation of about 5,200 meters (17,000 feet), and only 190 kilometers (120 miles) from the Pacific Ocean.
Like mothers, like daughters.... Two of the tributaries of the Amazon, the Juruá and the Madeira Rivers, are both over 3,300 km (2,060 miles) long. About 1,100 other tributaries empty into the Amazon River.
Talk about a big mouth!! The mouth of the Amazon is over 320 km wide (approximately 200 miles), and contains the worlds largest freshwater island, Marajó Island, with an area of 48,000 km2.
Momma was not a Rolling Stone! After leaving the Andes, the elevational gradient of the Amazon is very low. At Iquitos, Peru, still some 3,600 km (2,250 miles) from the Atlantic, the river-level at low-water season is only about 100 m (a bit more than 300') above sea-level, and the slope is around 2 cm (less than one inch) vertical change per kilometer. In the lower Amazon, at the mouth of Rio Negro and still 1,500 km from the Atlantic, the river-level at low-water season is only 15 m (~47') above sea-level, and the slope is about 1 cm per kilometer.
NEWS FLASH!! Rumpelstiltskin Drowns in Slow Flood. The Amazon is not a good place to fall permanently asleep on the river bank! Seasonal water levels can vary up to 20 meters (65 feet) in the middle Amazon region. Towards the mouth of the Amazon, the yearly change becomes less and less, but even near the mouth of the Amazon (at the Rio Xingu), it is still 4 meters (12 feet).
Flooded but not drowned. The seasonal variation in water levels means that huge areas along the major rivers in the Amazon basin are periodically flooded. The total area of flooded, or varzea, forest is between 50-60,000 km2, or about 4% of the total area of the Amazon rainforest. These flooded forest areas may extend as much as 80 kilometers (50 miles) from the main river channels, and the forest vegetation of the varzea is well adapted to being seasonally flooded. The structure and species composition of the varzea is very different from non-flooded upland (or terra firme) forest areas. Varzea forest areas are critical to the freshwater fisheries of the Amazon Basin.
Go with the flow. Despite the low slope of the Amazon, the river currents can be surprisingly strong. In the lower Amazon (with the lowest slope), current speeds range from 0.5-1.0 meters per second at low water, and twice that at flood stage. In localized areas, current speeds can reach as high as 3 meters (9.8 feet) per second.
Ships on a submarine river?? The width of the Amazon at Iquitos, Peru (3,600 km/2,250 miles from the ocean) is about 2 km. Ocean-going ships can easily access the Port of Iquitos at high water, as the mean depth of the current-canal of the Amazon is between 40 and 50 m (or up to 150+ feet deep), and in places, over 100 m (over 300 feet) deep. Even hundreds of miles away from the ocean, sections of the bottom of the river channel actually lie below sea level!