From Gödel, Escher, Bach by Douglas Hofstadter:

A friend said to me, "My uncle was almost President of the U.S.!" "Really?" I said. "Sure," he replied, "he was skipper of the PT 108." (John F. Kennedy was skipper of the PT 109 (http://en.wikipedia.org/wiki/Motor_Torpedo_Boat_PT-109).)

In everyday thought, we are constantly manufacturing mental variants on situations we face, ideas we have, or events that happen, and we let some features stay exactly the same while others "slip". What features do we let slip? What ones do we not even consider letting slip? What events are perceived on some deep intuitive level as being close relatives of ones which really happened? What do we think "almost" happened or "could have" happened, even though it unambiguously did not? What alternative versions of events pop without any conscious thought into our minds when we hear a story? Why do some counterfactuals strike us as "less counterfactual" than other counterfactuals? After all, it is obvious that anything that didn't happen didn't happen. There aren't degrees of "didn't-happen-ness." And the same goes for "almost" situations. There are times when one plaintively says, "It almost happened," and other times when one says the same thing, full of relief. But the "almost" lies in the mind, not in the external facts.