Surely, You Can't Be Serious
I think you could make a case for Airplane! -- without or without the exclamation mark on the end of the title -- as being the funniest movie comedy ever made. If it's not number one (and feel free to hash it out in the comments below), then certainly in the top ten. For better or worse, it's also the comedy that ushered in the modern ironic age. (See also headline above.)
Many of Airplane's (Airplane!'s?) fans know that it was based on a mid-1950s film called Zero Hour!, based on a novel by Arthur Hailey, who would go on to write Airport in 1968, adopted into the mother of all '70s disaster movies by Universal two years later. Zero Hour! starred Dana Andrews as a washed up fighter pilot named Ted Stryker, Sterling Hayden in the control tower, and then-L.A. Rams star running back Elroy "Crazylegs" Hirsch as Kareem Abdul-Jabbar, and played deadly, earnestly, straight. So straight that when the Zucker Brothers, coming off their debut Kentucky Fried Movie taped this film off the late-night movie show in the late 1970s, they knew there was the basis for a comedy. But to get a sense of how much the Zuckers stuck to the script of the original film (which they bought the rights to, so as to avoid getting sued) check out this YouTube clip, which cross-cuts between the original and in this case, it's far superior imitation -- the one substitute you should definitely accept.
And stop calling me Shirley. (Sorry, it was inevitable.)