It's uncertain where the Ouija Board first originated, but if you think Parker Brothers came up with this idea, you would be wrong. According to some, something resembling a Ouija Board was in 1200 B.C. China, a divination known as Fu Ji. Others claim Pythagoras, in 540 B.C., would conduct seances at "a mystic table, moving on wheels, moved towards signs" in which he and his pupil, Philolaus would interpret to the audience as revelations from the spirit world. Both historic claims have come under debates as being inaccurate.
However, talking boards weren't actually used until the Spiritualism movement in the 19th Century. The Fox sisters developed a system of knocks for each letter of the alphabet to supposedly communicate with spirits. Many wanted to mimic their methods and speak to ghosts too. There were many forms of divinations to spell out messages at that time, including swinging a pendulum over a plate that had letters around the edge or using an entire table to indicate letters drawn on the floor, but during the late 1800s, a device known as a planchette would be the beginning of it all.
At first, it was being sold as a novelty. Then, businessmen Elijah Bond and Charles Kennard came up with the idea to attach a board with the alphabet to the planchette (a device still used by some til this day) and patent it. This was to be the first Ouija Board. While Kennard helped start it all, it was one of his employees, William Fuld who kept it going. In 1901, he began production on his own boards simply called "Ouija" which he also acquired a patent for. Many tried to cash in on this innovated idea from 1920s to 1960s by producing and marketing their own design of talking boards. But Fuld was determined to keep the name "Ouija" and its concept from their grasps by suing many companies right up til his death in 1927. Who was to later buy Fuld's business from his estate? Well, Parker Brothers, now known as Hasbro, snatched it up in 1966 and I guess as they say the rest is history.
There are many theories as to why you shouldn't use a Ouija Board. Some paranormal investigators believe as you attempt to contact spirits you open a door that allows any of them to enter, good or bad. Some people say you will be killed or disappear if you use one. While others consider it harmless.
Sources: Wikipedia and Castle of Spirits