Retronaut has a nice collection of iconic photographs and the photographers who took them...
The set is a nice example of "Decisive Moment" images - the photos were not staged, and were fleeting instances; a moment sooner or later and the image wouldn't exist.
That concept seems to be very misunderstood, if you can judge by the Flickr Groups where people submit photos that they think are their "Decisive Moment" photos.
Of course, it's very easy to see the Decisive Moment in photos of famous events in history, because we know exactly how fleeting some of those moments were and how a combination of luck and smarts caused the photographer to click the shutter at exactly the right moment.
Photos where the scene and subject are unknown to us are harder, but Cartier-Bresson was a master of those; there's always something in the photo that tells us that the picture wasn't staged; for example, the iconic Bresson photo of the man jumping the puddle where he's captured mid-jump makes it obvious that this was a spur-of-the-moment, "click or you'll miss it" shot.
The Daily Mail has a nice collection of "Decisive Moment" photos (most if not all fit that category) taken by a young Stanley Kubrick when he was a photographer for Look magazine in the 40s and 50s. Most of those subject are unknown, but you can tell by the shot that it captures a singular moment of mood or action that existed and was gone in an instant.
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