The building with the most stories (in the literal sense of floors) is the Burj Khalifa in Dubai, which has 163 floors, making it the tallest building with the highest number of floors completed as of now

. However, if the question is posed as a riddle, the answer is "the library," playing on the word "stories" meaning both floors of a building and tales or books contained within

. So, factually, the Burj Khalifa has the most floors, but the riddle answer is the library.