Shakespeare invented thousands of words and coined hundreds of phrases like "eaten out of house and home," which appears in print for the first time in Henry IV Part 2 when Mistress Quickly complains that Falstaff "hath eaten [her] out of house and home" (2.1.12). (Source)
The publisher of the 1600 Quarto edition of the play jazzed up Shakespeare's plain title (and it's kind of a mouthful): "The Second part of Henry the fourth, continuing to his death, and coronation of Henry the fifth. With the humours of Sir John Falstaff and Swaggering Pistol. As it hath been sundry times publicly acted by the right honourable, the Lord Chamberlain his servants." (Source)
The character "Sir John Falstaff" was originally named "Sir John Oldcastle" in Henry IV Part 1. When the descendants of the historical Sir John Oldcastle made a fuss, Shakespeare changed the name of his fat, disgraceful knight to "Falstaff." The Epilogue of King Henry IV Part 2 makes a disclaimer about the character and promises that there's no relation to Oldcastle. (Source: Falstaff, ed. Harold Bloom, New York: Chelsea House, 1992.)
Giuseppe Verdi's opera, Falstaff, is based on the antics of, you guessed it, Sir John Falstaff. Mistress Quickly, Bardolph (whose cool Italian name is "Bardolfo") also make an appearance.