Burj Khalifa (برج خليفة "Khalifa Tower") was officially opened overnight (8pm Dubai time, Monday 04 January 2010). It is the world's tallest human-built structure at 828 m (2,717 ft) (those deep sea platforms anchored towards the sea-floor apparently don't seem to count).
Associated Press vision of the opening
Burj Khalifa towers over the previous tallest, Taipei 101, which was only 509.2 m (1,671 ft). Of course, there was a high price paid for its construction, particularly by migrant workers from southeast Asia (see BBC News report).
The National (United Arab Emirates) has reported that there are plans to build an even taller structure, at 1.1 km tall, in Saudi Arabia called Kingdom Tower.