After 300 years metal constructions such as the Eiffel Tower or steel bridges will start to break since for all these years there won't be anybody around to paint and protect from erosion. Steel rods and armed concrete will bloat up to three times of their initial thickness and the last tall building will go down. Vast swamps will reappear and hundreds of birds and animal species will return to their unfairly taken home. Large marine animals will also be very glad not to see us and with the absence of humans whales will thrive. This is what modern cities will look like after 500 years without people.
After 10.000 years the only reminiscing that people were here some day will be the remains of a few stone constructions, among with the pyramids of Egypt and the Great Wall of china. Mount Rushmore is said to be there for hundreds of thousands of years. In 50.000.000 years, plastic bottles and pieces of broken glass will be the last traces of our civilization.
In another 50.000.000 years they will be gone as well. We can say our planet is quite sturdy and can get rid of all our trash. If after 300.000.000 years or later there will be a new rational species, they might not even notice there was a civilization before.
So.... Our planet can perfectly do without us but we can't without her. Save The Planet!