Perhaps you have read the long-lived story perennially circulating since the President Kennedy assassination which purports to demonstrate "amazing coincidences" between that event and the Lincoln assassination one century previous. The endlessly forwarded email attachment that I received (Feb. 2008), titled "crazy history story," leads with an injunction: "Have a history teacher explain this--if they can." Feeling personally challenged, I began thinking about visiting the respective presidential libraries (Boston and Springfield) to begin many months of historical research to investigate the veracity of the claims. However, being a prudent investigator who understands the importance of evaluating resources at one's disposal to carry out research, I instead visited snopes.com at http://snopes.com/history/american/lincoln-kennedy.asp This Snopes specializes in debunking urban legends and provides an adequate explanation of the Lincoln-Kennedy "amazing coincidences" hoax, rating it "unclassifiable veracity."
Snopes labels the account as a catalog of "mere superficial coincidences that fail to touch upon the substantial differences and dissimilarities that underlie them." For example, I have read elsewhere that some medical historians claim that Lincoln exhibited symptoms of Marfan syndrome, which explains the abnormal elongation of his limbs. How does one compare this disorder of Lincoln's (if true) to Kennedy? This is the problem inherent in a list of "coincidences": there are myriads of other facts that might be more salient, but are not comparable in any meaningful way.
What for me is an even more interesting question is why we seem to have a need to believe such "amazing coincidences" in the first place? Anthropologist Pascal Boyer has written that we see purpose, intention and design even when they are not there. He calls it hypertrophy of social cognition. It is a hypersensitivity to agency, in that we attribute intention (by Providence, God, the Universe, Divine intervention) where only randomness exists. Have you ever seen faces in clouds? People claimed to have seen Satan in the billowing smoke issuing from the World Trade Center on 9/11. Our imagination creates what is not there outside our imagination. Humans have an overdeveloped sense which creates patterns in randomness. When people are shown a string of heads and tails produced by a random-number generator, they tend to believe they are not truly random--they look too orderly and thus rigged.
This is not to assert that there is not considerable nonrandomness in the world, but to answer the question of why we are inclined to believe a catalog of supposed "amazing coincidences?" The answer seems to be that we want to believe there are deeper meanings in our everyday lives and in historical events, meanings that dispel what otherwise seems to us to be reality too random and lacking sufficient purpose and meaning. We do not want to feel our lives are random and purposeless; we would like to believe that we as individuals lead lives that are filled with amazing coincidences. And, if we can detect nonrandomness within historical events, then we feel we are justified in believing that everything--including our own lives--are actually much more than just random acts of a random-number-generator Universe. We desperately want to believe that "amazing coincidences" are actually attributes and acts of an Amazing Creation--and we are its amazing nonrandom Acts.