Taipei 101 is the pride of Taiwan, standing at 509 m (1,671 ft). Opened in 2004, it remains the world's tallest building for now. (For the record, the Sears Tower is higher with its antennae and the CN Tower is the worlds tallest non-habitable structure).
Actually having 101 floors (hence the name), it boasts of the world's fastest elevator and has an observable tuned mass damper or giant pendulum on the 92nd floor. The pendulum is made to counteract the effects of high winds, typhoons and earthquakes acting on the building and that are common to Taiwan.
Here's something that's often overlooked. 101 actually has an open air observation deck above the enclosed one. The sides are barred by a cage but the top is open and, man, is it winding up there! The wind whistles through the bars to create an eerie sound.
Visit the tower on a pre-typhoon day for the best viewing. Before a typhoon arrives, the particulate in the air gets sucked away and there is glorious sunshine! I've heard the night view is good too. Also, people try to get a good view of the moon at Moon Festival time.
New Years Eve has fantastic fireworks shooting off the building as well if you can get through the impenetrable crowds to get near the building.
On another note, Taipei residents joke about working in the tower. Deep down I think they are scared. I always joke that if my company started a branch there and asked me to work there I would quit.
Locals also complain about its shape. They think it looks ugly. I've also heard that its fengshui is bad since it faces mountains on one side. This is hard to believe since it is almost an impossibility that such a grand project would have not consulted a fengshui master before construction.
If you are a really determined visitor, you could try the annual run up the tower for charity. You won't find me there!