Story behind the song according to ShareFaith.com:
"Robert Robinson (1735-1790) was eight years old at the time of his father's death. He was a very bright, headstrong boy who became increasingly more difficult for his mother to handle. When Robert turned 14, she sent him to London for an apprenticeship with a barber. Robert proceeded to get into even more trouble, taking on a life of drinking and gambling.
"At 17, Robert and some of his drinking buddies decided to attend an evangelistic meeting, with a plan to make fun of the proceedings. When George Whitfield began to preach, Robert felt as if the sermon was just for him. He did not respond to the altar call that night, but the words of the evangelist would haunt him for the next three years.
"On Dec. 10, 1755, at age 20, Robert finally yielded his life to Christ, and very soon thereafter answered a call to the ministry. Three years later, as he was preparing to preach a sermon at the Calvinist Methodist Chapel in Norfolk, England, Robert wrote Come Thou Fount of Every Blessing to complement his sermon. The music for the hymn was composed by Asahel Nettleton in 1813."