As far as jet-powered civil airliners are concerned the 737 series holds the title by far, so much as I am aware.
However, many other aircraft have had longer production runs:
Douglas DC-3 - 13,400 aircraft
Consolidated B-24 - 18,482 aircraft
Boeing B-17 - 12,726 aircraft
Messerschmitt Bf.109 - 35,000 aircraft
Just to name a few, but by no means a complete list. I'm sure there is a comprehensive ranking floating around out there somewhere.
Too often we ... enjoy the comfort of opinion without the discomfort of thought. - John Fitzgerald Kennedy