score:22
The oldest confirmed use of any version of this quote that I was able to find is from Ray Cummings' short story The Time Professor, published in the Jan. 8, 1921 issue of Argosy All-Story Weekly (thanks to mgkrebbs for pointing this one out):
"I do know what time is," Tubby declared. He paused. "Time," he added slowly -- "time is what keeps everything from happening at once. I know that--I seen it in print too."
Pg. 371 - Emphasis mine - Ray Cummings - Google Books
He used it again in his novel The Girl in the Golden Atom, published in 1922:
The Big Business Man smiled. "Time," he said, "is what keeps everything from happening at once."
Ch. 5 - Ray Cummings - Project Gutenberg - Public Domain
This quote has been mistakenly attributed to Albert Einstein, Richard Feynman, Woody Allen, John Archibald Wheeler, and likely others, in many different forms.
EDIT: Added an earlier use of the term by the same author.