I've heard many places, although I haven't independently verified it, that it wasn't until the invention of the elevator that towers were really valued for what we use them for today and the high floors were often cheaper.
Towers were mainly defensive structures. A tower would provide a commanding view of the surrounding area, and give archers and missile weapons substantial advantage. They were also somewhat intimidating and a display of wealth/power/prestige.
Like walls they were vulnerable to sapping - digging under the structure and causing it to collapse. More so than walls due to their height. And later, cannon fire. Which is why along with castles they started going out of favour about the 16th century, except as cheap observation posts, such as on borders, and non-military structures such as lighthouses.
As living quarters, much like castles they were not as practical as simpler manor homes. But in a very violent, somewhat lawless era, they were often used by the wealthy/powerful.
