As believed now, this invention is one of the most life-saving car enhancements besides the seat belt.
Background info
The windshield/windscreen wiper was invented in the year 1902, by Mary Anderson (born in Alabama, USA), and was one of the first car-related inventions made by a woman. She's often confused with her Swedish-born namesake, who was a famous labor organizer in the 1920's. Many more women would later work on inventions for cars as well, most of them worked on safety enhancing inventions like roadsigns &c. She received a patent in the year 1905, and her invention was standard equipment on almost any car from 1913 onwards.
How it came to be
It is said she was touring New York in an automobile and felt sorry for the nearly freezing driver, who continually had to stop and wipe of the snow from his windshield. When she got home she drawed a rough design of a swinging arm that could be operated with a lever from within the car.
At first, like with many of the most practical inventions, her idea was discarded by friends and relatives. But she persisted and that made it the success story it is today. The windshield wipers are now in the same impressive list of most important inventions as the Aeroplane, Laser, Typewriter etc.
Initially she designed the wiper to clear the windshields of ice and snow without the driver having to get out of the car all the time. The driver could remove the wipers easily when the weather got warm enough. In time, the system evolved and got a second arm, the arms were able to move faster and were built into the car itself. These developments made them useful to wipe of water as well.