This is an iconic building for Taipei and a must see for tourists. We went on a weekday evening and the queue moved really quick even though it looked quite long. Tickets are relatively cheap and the views are great. The elevator ride itself is impressive and the speed of its operation.
The views are fantastic from the tower and seeing the way they built it to withstand an earthquake is really impressive, including the suspended ball in the centre to prevent swaying of the tower. There are free headsets to give you a narration of the building which was quite interesting.
Worse part were the tacky stores selling red coral jewellery (of all things) and the rude and aggressive mainland Chinese and Korean tourist groups (and their leaders with megaphones).
All in all, a must see in Taipei!