1 day after people
The special assumes that humanity disappears suddenly and immediately, but does not speculate what would cause such an event.
Fossil fuel fired power plants, which are largely automated, would remain running for a few hours until their fuel supplies are depleted. Within hours, lights begin going out all over the world as electrical systems start failing, due to lack of maintenence.
Subway systems like the New York City MTA require pumps to keep the groundwater at bay and without humans to turn them on, most subways will be flooded within 36 hours.
After 48 hours, nuclear power plants will enter a safe mode automatically and will not meltdown. Wind turbines will cease operation once their lubrication fails.
All areas except those powered by hydroelectric dams lose their functioning.
10 days after people
Food would rot in grocery stores and in refrigerators. While meltwater from freezers or food on counter tops could provide temporary sustenance, pets would need to leave the house or die of starvation. Those which were not trapped would start to compete for food. Dogs and cats that were bred by humans for appearance now have no niche in this new competitive environment and will die first. For example, the short legs and small mouths of bulldogs or terriers will be handicaps for them.
6 months after people
Smaller forms of wildlife not normally seen in civilization like coyotes and bobcats begin to inhabit suburban areas. Deer begin grazing in neighborhoods as well. Rats and mice have consumed our edible supplies and are leaving urban areas to go back into the wild.
2 years after people
The Hoover Dam would stop generating power when mussels clog coolant pipes. Las Vegas, Nevada, one of the last areas with some artificial illumination, would then become completely dark. The Colorado River downstream from the dam would temporarily dry up as the flow of water through the dam stopped; when the level of Lake Mead reached the spillways around the dam, the normal flow would resume.
Humanity's final radio and television signals which have been traveling through outer space have now deteriorated into undetectable background radiation, according to scientists with the SETI project.
5 years after people
Plant life will have sprouted and covered many surfaces in urban areas with vines, grasses, and tree saplings.
20 years after people
The ruins of Prypiat, Ukraine, which was abandoned in 1986 due to the Chernobyl disaster documents the level of decay which could happen after twenty years of humanity's disappearance. Despite the radiation levels, many animal populations have grown significantly in areas humans have left. Plants have grown in many structures once used by humans.
25 years after people
Sea water floods into cities such as London and Amsterdam which are currently kept dry by human engineered projects. Windows in high rise buildings begin to crack and shatter due to the cycle of freezing and thawing and the decay of window sealants. Cockroaches will die off without warmth created by humans, except for those that went underground. Wolves will repopulate the United States by half a million
50 years after people
By this time, many wooden frame houses would have burned, rotted, or been largely consumed by termites. Trees and vines grow into remaining brick and masonry elements, which would also be weakened by salts. Compacted earth dams may begin to fail due to widening leaks.
75 years after people
Many of the roughly 600 million automobiles on earth would be reduced to only a pile of metal. Some automobiles in arid climates would not suffer the effects of corrosion, and would still be recognizable. While the rubber tires of cars would have deflated and gone flat years ago, they would not corrode or decompose for centuries.
100 years after people
Large bridges such as the Golden Gate Bridge and the Brooklyn Bridge would collapse due to corrosion of support cables.
150 years after people
Many streets in Manhattan collapse into the flooded tunnels below. Many large buildings are completely colonized by plants and animals and resemble a wild landscape.
200 years after people
Large structures such as the Empire State Building, Sears Tower, Space Needle, and Eiffel Tower would collapse due to corrosion, invasive plant life, and ground water destabilizing their foundations.
500 years after people
Items made with modern concrete would give way as the steel rebar reinforcing them expands to three times its original size as it rusts.
1,000 years after people
Most modern cities would be destroyed and/or covered in flora, with collapsed and fallen skyscrapers becoming new mounds and hills. Manhattan would appear much as it did before human settlement with old streams and bodies of waters returning. There would be little evidence that a human civilization existed on earth. Certain structures made out of thick rock or concrete, like the Egyptian Pyramids or medieval castles, might survive with minimal damage.
10,000 years after people
The Hoover Dam, one of the last remnants of advanced civilization, will fail due to erosion of its concrete and the cumulative effect of seismic activity.
By this point, any substantial evidence of humanity's former domination over nature would be all but gone. Only a few things would survive, such as large stone structures. The Pyramids at Giza remain, but would be mostly buried by the Sahara Desert's sands. Portions of the Great Wall of China may also remain intact. The faces at Mount Rushmore might also survive, and may remain so for hundreds of thousands of years to come.
Modern forms of information storage like hard drives, compact disks, DVDs, photographic film, and paper would have long since decayed.