Looks like it was the DC3. 

#2 is the B737 which is the most popular jetliner.

Under 5,000 produced do not make the list.

There is only one ultralight, the Weedhopper

 

Cessna 172	C	Utility / trainer	44,000+[1]	United States	1956	present	Also built in France by Reims Aviation.
Ilyushin Il-2	M	Ground-attack	36,183	Soviet Union	1941	1945	Most-produced combat aircraft; most-produced low-wing aircraft; most-produced aircraft for over half a century until surpassed by the Cessna 172 in the 2000s.[verification needed]
Messerschmitt Bf 109	M	Fighter	34,852	Germany	1936	1958	Most-produced fighter and single-seat aircraft. Also built in Hungary, Romania, Spain, Czechoslovakia and Switzerland.
Piper PA-28 series	C	Utility / trainer	32,778+	United States	1960	present	Sold as Cherokee, Cherokee Warrior, Cherokee Pathfinder, Warrior, Archer, Dakota, Cadet, and Pilot.
Cessna 150 / 152	C	Utility / trainer	31,471[2]	United States	1958	1986	Most-produced two-seat civil aircraft. Also built in France (both models) and Argentina (150 only). 23,887 150s, 7,584 152s.[3]
Cessna 182	C	Utility	23,237+	United States	1956	present	Also built in France.
Supermarine Spitfire/Seafire	M	Fighter	22,685	United Kingdom	1938	1948	20,351 of total were land-based Spitfires. The first Seafires were Spitfires modified with tailhooks.
Piper J-3 Cub	C	Utility / trainer	20,191[4]	United States	1938	1947	Most-produced fabric-covered monoplane. Includes military variants such as L-4, O-59, TG-8 and NE. 150 built in Canada.
Focke-Wulf Fw 190	M	Fighter	20,051	Germany	1939	1945	64 produced in post-WWII France as the "NC 900".
Polikarpov Po-2	M	Biplane, multirole	20,000[5] to 30,000[6]	Soviet Union	1928	1952[6]	Most-produced biplane. Used for training, reconnaissance, liaison, and ground-attack. Also built in Poland.
Consolidated B-24 Liberator	M	Heavy bomber	18,482[7]	United States	1940	1945	Most-produced heavy bomber and multi-engine aircraft. Includes 962 built by Douglas,[8] 6,792 by Ford Motor Company and 966 by North American. Does not include related PB4Y-2 Privateer.[7]
Antonov An-2 / An-3	C	Biplane, utility / agricultural	18,000+	Soviet Union	1947	2009	Most-produced transport; longest production run of any transport aircraft. Also built in China and Poland.
Mikoyan-Gurevich MiG-15	M	Jet fighter	18,000+	Soviet Union	1947	1950s	Most-produced jet. Also 3,454 built in Czechoslovakia; 727 in Poland; and an unknown number in China.
Mil Mi-8/Mi-17	M	Helicopter, utility	17,000+	Soviet Union	1961	present	Most-produced helicopter.
Beechcraft Bonanza	C	Utility	17,000+	United States	1947	present	Longest continuous production run of any airplane in history.[9][10][11] Includes Debonair variant; excludes dissimilar Twin Bonanza.[12]
Yakovlev Yak-9	M	Fighter	16,769[13]	Soviet Union	1942	1948
Douglas DC-3	C	Airliner / transport	16,079	United States	1935	1952	607 built as civil airliners; 15,472 built as military transports, including the Soviet Lisunov Li-2 and Japanese Nakajima L2D; after World War II, most converted into civil airliners or freighters.
Bell UH-1 "Huey" Iroquois	M	Helicopter, utility	16,000+	United States	1959	1987
Republic P-47 Thunderbolt	M	Fighter	15,660[14]	United States	1942	1945
North American P-51 Mustang	M	Fighter	15,586	United States	1940	1951	Excludes F-82 and other derivatives.
North American T-6 Texan	M	Trainer	15,495	United States	1937	1950s	Includes SNJ and Harvard. Also built in Canada.
Junkers Ju 88	M	Multirole	15,183 [15][page needed]	Germany	1939	1945	Luftwaffe multirole bomber, heavy fighter and reconnaissance aircraft.
Hawker Hurricane	M	Fighter	14,487	United Kingdom	1937	1944	Also built in Belgium, Canada and Yugoslavia.
Mikoyan-Gurevich MiG-21	M	Jet fighter	13,996	Soviet Union	1959	2006	Most-produced supersonic aircraft. According to the Guinness Book Of Records it is the most-produced jet-powered military aircraft.[16] Also built in China, Czechoslovakia and India.
Waco CG-4	M	Glider, military	13,903+	United States	1942	1945	Most-produced glider. Many licensed manufacturers.
Curtiss P-40 Warhawk	M	Fighter	13,738[17]	United States	1939	1944
Chotia Weedhopper	C	Ultralight	13,000+	United States	1977	2012	Most-produced ultralight.
Boeing B-17 Flying Fortress	M	Heavy bomber	12,731	United States	1937	1945	3,000 built by Douglas,[8] also produced by Lockheed Vega.
Vought F4U Corsair	M	Fighter	12,571	United States	1941	1952	Many built as Goodyear FG or Brewster F3A.[18] Longest production run of any U.S. piston-engined fighter.
Grumman F6F Hellcat	M	Fighter	12,275	United States	1942	1945
Vultee BT-13 Valiant	M	Trainer	11,537	United States	1939	1947
Vickers Wellington	M	Medium bomber	11,462[19]	United Kingdom	1936	1945
Petlyakov Pe-2	M	Dive bomber	11,427	Soviet Union	1939	1945	Most-produced dive bomber of any type – a twin-engined design.
Avro 504	M	Biplane, bomber / trainer	11,303[20]	United Kingdom	1913	1940[21]	Most-produced World War I aircraft design. Includes Japanese and Soviet production.
Boeing 737	C	Jet airliner	11,022[22]	United States	1967	present	Most-produced jet-powered civilian aircraft. Includes the original, Classic, NG, and MAX models, as well as military variants such as the C-40 and P-8.[citation needed]
Avro Anson	M	Multirole	11,020[23]	United Kingdom	1935	1952	Also built in Canada.[23]
Mooney M20	C	Utility	11,000+	United States	1955	2019
Mitsubishi A6M Zero	M	Fighter	10,939	Japan	1940	1945
Piper Pacer	C	Utility / trainer	10,610[24][25]	United States	1950	1964	Includes PA-20 Pacer and PA-22 Tri-Pacer and Colt.
Mikoyan-Gurevich MiG-17	M	Jet fighter	10,367	Soviet Union	1951	1986	Also built in Poland and China; many built as the Shenyang J-5 / JJ-5.
Airbus A320 family	C	Jet airliner	10,359[26][27]	Various European	1988	present	Consists of the A318, A319, A320 and A321. Designed and built in France, Germany, Spain and the UK, with additional assembly in China and the U.S.
Polikarpov I-16	M	Fighter	10,292[28] [verification needed]	Soviet Union	1934	1943	Also manufactured in Spain and China.
Piper PA-18 Super Cub	C	Utility / trainer	10,222[29]	United States	1949	1983	Includes military variants such as L-18 and L-21.
Lockheed P-38 Lightning	M	Fighter	10,037	United States	1941	1945	Two-engined twin-boom design.
Aeronca Champion	C	Utility / trainer	10,000+	United States	1946	2019[30]	Includes military L-16. Several changes in manufacturer.
DFS SG 38 Schulgleiter	M	Glider, trainer	10,000~[31]	Germany	1938	1944
North American B-25 Mitchell	M	Medium bomber	9,984	United States	1939	1945
Lavochkin La-5	M	Fighter	9,920	Soviet Union	1942	1944
North American F-86 Sabre / FJ Fury	M	Jet fighter	9,860	United States	1947	1956	Also built in Australia and Canada.
Grumman TBF Avenger	M	Torpedo bomber	9,836[32][33]	United States	1941	1945	Includes 7,546 built as TBM Avenger by General Motors.[33]
Bell P-39 Airacobra	M	Fighter	9,584	United States	1938	1944
Cessna 210	C	Utility	9,240	United States	1957	1986
Beechcraft Model 18	C	Utility	9,000+	United States	1937	1970	Includes military variants such as C-45, AT-7, and SNB.
Airspeed Oxford	M	Trainer	8,751[5]	United Kingdom	1937	1945	Several manufacturers.
Yakovlev Yak-1	M	Fighter	8,734[34]	Soviet Union	1940	1944
Boeing-Stearman Model 75	M	Biplane, trainer	8,584[35]	United States	1934	1942
Cessna 206	C	Utility	8,509+ or 7,783+[citation needed]	United States	1962	present	Includes models 205 and 207.
SPAD S.XIII	M	Biplane, fighter	8,472	France	1917	1918	Most-produced World War I fighter aircraft design.
La Mouette Atlas	C	Hang glider	8,000+	France	1979	present	Most-produced hang glider.
Grumman F4F Wildcat	M	Fighter	7,885[36]	United States	1937	1943	Includes about 5,600 built as FM Wildcat by General Motors.[37]
Piper PA-32	C	Utility	7,842+	United States	1965	2007	Enlarged PA-28 sold as Cherokee Six and Saratoga.
Breguet 14	M	Reconnaissance	7,800	France	1916	1928	2,300 built after WWI.
de Havilland Mosquito	M	Multirole	7,781	United Kingdom	1940	1950	Also built in Australia and Canada.
Fairchild PT-19	M	Trainer	7,700+[38]	United States	1938	1948	Includes variants PT-23 and PT-26. Also built in Canada and Brazil.
Cessna 120 and 140	C	Utility / trainer	7,664[39][40]	United States	1946	1950	Developed into Cessna 150.
Republic F-84 Thunderjet	M	Jet fighter-bomber	7,524	United States	1946	1953	Excludes swept-wing F-84F / RF-84F derivatives.
Douglas DB-7 (A-20 Havoc)	M	Multirole	7,478[41]	United States	1938	1944	Includes 380 built by Boeing.[42]
Avro Lancaster	M	Heavy bomber	7,377	United Kingdom	1942	1945	Includes 430 built under licence in Canada.
Bell 206 JetRanger	C	Helicopter, utility / trainer	7,340+	United States	1966	2017	Also made in Canada and Italy.
Heinkel He 111	M	Medium bomber	7,300	Germany	1935	1944	Also built in Spain as the CASA C.2111.
Yakovlev UT-2	M	Trainer	7,243	Soviet Union	1936	1944
Curtiss SB2C Helldiver	M	Dive bomber	7,140	United States	1940	1945	900 built as A-25; 1,194 built in Canada.[43] Most-produced single-engine dive bomber.
de Havilland Tiger Moth	C	Biplane, trainer	7,105	United Kingdom	1931	1944	Also built in Canada, Australia and New Zealand.
Polikarpov R-5	M	Reconnaissance / bomber	7,000	Soviet Union	1928	1937
Piper PA-23	C	Utility / trainer	6,976[44]	United States	1952	1981	Sold as Apache and Aztec.
Beechcraft Baron	C	Utility	6,884+[12]	United States	1961	present	Includes 55, 56, 58, and sub-variants such as military T-42; excludes related Travel Air.[12]
Curtiss JN-4	M	Biplane, trainer	6,813	United States	1915	1927
Polikarpov I-15	M	Biplane, fighter	6,750[45]	Soviet Union	1933	1940	Also built in Spain.
Tupolev SB	M	Bomber	6,656	Soviet Union	1936	1941	Also built in Czechoslovakia.
Ilyushin Il-28	M	Medium bomber	6,635+	Soviet Union	1949	1955	Also built in China and Czechoslovakia.
Yakovlev Yak-18	M	Trainer	6,630+[46]	Soviet Union	1946	1960s	Also produced in Hungary and China. Production claims vary from 6,168 including 125 Yak-18P and 25 -18PM[47] to 6,630 excluding P and PM.[46] Both exclude unrelated Yak-18T.
Lockheed T-33 Shooting Star	M	Jet trainer	6,557	United States	1948	1959	Also built in Canada by Canadair.
Yakovlev Yak-7	M	Fighter / trainer	6,399[48]	Soviet Union	1940	1943
Robinson R44	C	Helicopter, utility / trainer	6,300+	United States	1993	present	Most-produced reciprocating engine helicopter.
Airco DH.4	M	Biplane, Bomber	6,295[49]	United Kingdom	1916	1926	1,449 in the UK[50] and 4,846 (as the DH-4) in the US.[51]
Lavochkin-Gorbunov-Gudkov LaGG-3	M	Fighter	6,258	Soviet Union	1941	1942
Ilyushin Il-10	M	Ground-attack	6,226	Soviet Union	1944	1954	Also built in Czechoslovakia as the Avia B-33 / CB-33.
Cessna 180	C	Utility	6,193[52]	United States	1953	1981	Developed into Cessna 182.
Handley Page Halifax	M	Heavy bomber	6,176[53]	United Kingdom	1940	1946
Cirrus SR22	C	Utility / trainer	6,150+[54]	United States	2001	present	Most-produced aircraft made of composite material; most-produced aircraft with production period starting in the 21st century. Developed from Cirrus SR20.
Messerschmitt Bf 110	M	Heavy / night fighter	6,150	Germany	1936	1945	Twin-engined design. Most sources state 6,000 to 6,150 produced.
Junkers Ju 87	M	Dive bomber	6,000	Germany	1935	1944
Sopwith 1½ Strutter	M	Biplane, multirole	5,939	United Kingdom	1917	1918	Majority built in France for French use.
Douglas SBD Dauntless	M	Dive bomber / scout	5,938[55]	United States	1940	1944	Includes A-24 Banshee variant.[55]
Bristol Beaufighter	M	Heavy fighter	5,928	United Kingdom	1940	1946	Also built in Australia.
Nakajima Ki-43	M	Fighter	5,919[56]	Japan	1942	1945
Yokosuka K5Y	M	Biplane, trainer	5,770[5]	Japan	1934	1945
Lavochkin La-7	M	Fighter	5,753	Soviet Union	1944	1946
Cessna 310	C	Utility / trainer	5,737[57]	United States	1954	1980
Antonov A-1	M	Glider, trainer	5,700	Soviet Union	1930	1940s
ERCO Ercoupe	C	Utility / trainer	5,685	United States	1940	1969	First civil aircraft with a nose wheel landing gear. Several changes in manufacturer.
Mikoyan-Gurevich MiG-19	M	Jet fighter	5,500[58]	Soviet Union	1953	1991	World's first mass-produced supersonic aircraft. 2,500 built in Soviet Union. Also built in China (~3,000) and Czechoslovakia.
Sopwith Camel	M	Biplane, fighter	5,497	United Kingdom	1917	1918
Mil Mi-2	M	Helicopter, utility	5,497	Soviet Union	1965	1985	Built in Poland.
Cessna AT-17 Bobcat	M	Trainer	5,422	United States	1939	1943
Bristol F.2 Fighter	M	Biplane, fighter	5,329	United Kingdom	1916	1927
Martin B-26 Marauder	M	Medium bomber	5,288	United States	1941	1945
Stinson 108	C	Utility / trainer	5,260[59]	United States	1946	1950
Ilyushin Il-4	M	Medium bomber	5,256	Soviet Union	1942	1944
Royal Aircraft Factory S.E.5	M	Biplane, fighter	5,205	United Kingdom	1917	1918
McDonnell Douglas F-4 Phantom II	M	Jet fighter-bomber	5,195[60]	United States	1958	1981	Includes 127 built in Japan by Mitsubishi.[60]
Cessna 170	C	Utility / trainer	5,174[61]	United States	1948	1956	Developed into Cessna 172.
Mikoyan-Gurevich MiG-23	M	Jet fighter	5,047	Soviet Union	1967	1985	Most-produced variable-sweep aircraft.
Yakovlev Yak-12	M	Multirole STOL	5,000+	Soviet Union	1946	1968

Edited June 26, 20223 yr by Fielder

Remarkable I suppose that the A320 family' has been in production for only 34 years whereas the B737 has been in production for 55 years, yet Airbus is a just few hundred frames behind Boeing.  And of course the B737 is in decline (ie I'm guessing there won't be another variant beyond the MAX) whereas the A320 family seem to have a secure future with plenty of orders for the A320 neo. It seems likely then that it wont be too many more years before the A320 family take the title, "Most-produced jet-powered civilian aircraft."

But stat's can be misleading so interested in anyone else's take on this. Also, why is the A320 referred to as a 'family' whereas the generations of Boeings are not?   Just a couple of my observations in the context of @Fielder's comprehensive and interesting list of aircraft production. Not trying to start a Boeing/Airbus moan.😬

Only one ultra lightweight met the over 5000 units produced criteria.

In utility/transport planes the JU-52 had about 4,800 made and so is off the list. 

I was astonished Russia cranked out 36,000 IL-2 during WWII (number 2 on the most produced aircraft list).