[End of Eternity][1](1955) is a novel with this plot. Asimov originally wrote it as a short story, it was not published at that time, but this original was later released in an anthology called "[The Alternate Asimovs][2]"(1986)

The basic idea was that humanity never developed atomic power and space flight, but discovered time travel technology instead. Since all new developement is being spent in time travel, and since the "Eternals", a cabal of human time travelers, aim to minimize wars and dangerous technologies by altering history, humanity never develops the technologies required to leave the solar system before the whole galaxy is colonized by different races, and humanity eventually dies out in this version of history.

>! Ultimately, history is altered so that humanity will colonize the galaxy before any other races have the chance to develop, which also prevents the discovery of time travel and the founding of the "Eternity" cabal.

The short story apparently has a slightly different plot and in particular a different ending than the novel. Asimov himself called it weak.

  [1]: http://en.wikipedia.org/wiki/The_End_of_Eternity
  [2]: http://en.wikipedia.org/wiki/The_Alternate_Asimovs