The best answer I can find is the Burj Khalifa in Dubai, which has 2,909 steps up to the 106th floor. The actual building has several more levels, but these don't have stairs and ladders are used for maintenance work. At just under 830 metres it is also the tallest building in the world. It is used for corporate events and as a luxury hotel, and is also set in the middle of enormous gardens.

The Burj Khalifa was completed in 2010 and is likely to remain the world's tallest building for some time.

For many years the tallest building was the Empire State Building, which has 1,860 steps. This isn't surprising as it has 102 floors and is over 380 metres high (which now makes it only the 15th tallest building in the world). The building is located in Manhattan in New York, USA.