An earlier question received interesting answers on what airplanes have been in service the longest; this question asks about airplanes in production the longest. By this, I mean from earliest production of the first variant, to the end of the production run of the latest variant. Thus, the 737 would count from 1967 through the present, even though there have been plenty of variants along the way.
Regarding breaks in production... EDIT: any break in production less than a decade, doesn't rule out an aircraft. Multiple breaks in production that total less than a decade of "down" time don't either. An aircraft that is essentially the same produced by somebody else is fine if both are generally regarded as being the same aircraft, even if the designation is different (i.e. the F4U was built by multiple manufacturers, but today everybody thinks of any of them as a Corsair).
Military, civilian, large & small, even including gliders & helos (if any have been in production long enough to be competitive) are all fair game. We can mention balloons (as "aircraft," though not really "airplanes") as having been produced since before the Wright brothers, but that's not really what I have in mind here. Edit: Nor is "oldest aircraft still in production," even though the answers tend to be similar since it looks like the aircraft mentioned there are still in production. This question is about length of production run, even if it is complete.
So, longest production run... what do we have?