Two of the four coincidences posted by John Steele Gordon at AmericanHeritage.com:
1) Probably the most famous coincidence in American history is that both Thomas Jefferson and John Adams died on the same day. And it was not just any day but July 4, 1826, the fiftieth anniversary of the adoption of the Declaration of Independence. The cherry on top is that Adams and Jefferson were the only two signers of the Declaration to later become President. We will never know, of course, but I’ve always suspected that both Jefferson and Adams, old and rapidly failing though they were (Adams was 90, Jefferson 83) were aware of what day it was and perhaps at some level decided that it was a good day to die. President James Monroe also died on July 4, in 1831. So more than 8 percent of deceased American Presidents have died on the nation’s birthday, and three of the first five did.
3) In the 1940s two of the mightiest and most iconic of American industrial corporations were General Motors and General Electric. The president of GM from 1941 until 1953 was a man named Charles E. Wilson. The president of General Electric from 1940 to 1950 (except from 1942 until 1945, when he worked for the government) was a man named . . . Charles E. Wilson. They were unrelated and were known as Engine Charlie and Electric Charlie to keep them separate. (Runner up in this category, perhaps, is the fact that Chief Justice Earl Warren was succeeded in office by Chief Justice Warren Earl Burger.)