A one string guitar would normally be viewed as a six string guitar with five strings missing, but there is an instrument that has only one string and that is the Diddley Bow.
The Diddley Bow originated from West Africa where children would play them by beating the string with sticks and changing the pitch by moving the slide up-and-down. It was a toy for children to play with but was also seen as an entry level instrument. Slaves in the United States would make them for children as toys and as they got older and proficient on the Diddley Bow they would move on to a real guitar. The popularity of the Diddley Bow never took off but was used in the deep south especially in the African-American community where the Diddley Bow influenced the development of the blues sound.
But the Diddley Bow never really made it into mainstream production in fact the Diddley Bow was home made out of all sorts of materials that were available. A common way of making a Diddley Bow was to fix broom wire from the top of the porch to the bottom, inserting a can or bottle to make a bridge and using a bottle neck slide to change the pitch.
Today Diddley Bows are still being used but not by many and they are still made from spare bits of scrap materials. Seasick Steve once said “this is a Diddley Bow. It's a bit of wood with a string nailed to it”.