Like Stuart Dren said, you don't have to have a map if you don't want to. Tolkien drew a map for
The Hobbit, and his son Christopher later helped him draw a map for
The Lord of the Rings, because it helped him imagine the topography and keep track of locations and distances as he wrote.
Robert E. Howard hand-drew maps of the Hyborian Age, the setting for his Conan stories. He used them to ensure consistency in the geographical details and ethnological background of his Conan stories.
On the other hand, Sir Terry Pratchett didn't commission maps of the Discworld until 1993 ("The Streets of Ankh-Morpork"), about 10-11 years after he wrote the first book in the series, because he found them a limit to his imagination. But he grudgingly accepted that he had to have maps, otherwise some smart-aleck would find some tiny niggling "error" and
complain.
In short (too late): you don't have to have maps if you don't want them. A map is like any author's tool (e.g. plans, beat sheets etc.). You can have one, but whether you reveal it to your readers is up to you. Let them revel in your artistic talent, or let them picture in their mind's eye what your world looks like. It's up to you.
