For those of you who don't know much about Sputnik, I've listed a few references at the end of this post. I also found this fascinating page, The New York Times on AOL: Sputnik, which the Times apparently put together for the fortieth anniversary ten years ago. It includes links to some of their original news coverage and audio files of Sputnik's signals.
The image of the Times's front page of October 5, 1957 pretty much sums up the event in its three-line, full width headline:
SOVIET FIRES EARTH SATELLITE INTO SPACE;
IT IS CIRCLING THE GLOBE AT 18,000 M.P.H.;
SPHERE TRACKED IN 4 CROSSINGS OVER U.S.
I wasn't alive at the time of the Sputnik launch, but I have read about how much it frightened Americans at the time. The fact that the Soviet Union hit this milestone before the United States did spurred the country into action. Suddenly, more funding was found for science education and for our own fledgling space program, and of course, when Kennedy was elected president in 1960, he set the goal for a manned moon landing before the end of the decade. The space race was on.
There's a lot I could discuss here, such as the Cold War paranoia that I and others of my generation experienced in our own lifetime, or the sad state of our space program after the Apollo missions ended. But instead, I'll leave analysis to others, and just mark this milestone with that sense of wonder at human achievement.
Look what we've done. Look what we can do.
Wikipedia: Sputnik Program
Wikipedia: Sputnik 1
NASA's Sputnik page