Everyone "knows" that Washington was the first of the (so far) 43 Presidents of the US. However, this isn't strictly the case. During the American Revolution, the Continental Congress (or the 'United States in Congress Assembled') chose Peyton Randolph as the first President. Under Randolph, one of their first moves was to create the Continental Army (in defence against Britain), appointing General Washington as its commander. Randolph was succeeded in 1781 by John Hancock, who presided over independence from Great Britain (see myth #6). After Washington defeated the British at the Battle of Yorktown, Hancock sent him a note of congratulations. Washington's reply was addressed to "The President of the United States". Eight years later, as a revered war hero, Washington himself became America's first popularly elected President - but strictly speaking, the FIFTEENTH President!
John Hancock & Peyton Randolph were presidents of the Second Continental Congress and the Congress of the Confederation. Peyton Randolph shouldn't be considered at all because - according to his own myth #6, the United States wasn't an independent state until 1783, hell it wasn't even a country, they were just "united States" - as it's written in the Declaration of Independence.
For 14 bonus points, I'll take Things Named after John Hancock for a thousand, Alex.