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For my own reference, the longest running Broadway shows as of August 19, 2007. The ones with an "*" are still running.
* "The Phantom of the Opera" 8157
"Cats" 7485
"Les Misérables" 6680
"A Chorus Line" 6137
"Oh! Calcutta!" (Revival) 5959
"Beauty and the Beast" 5461 (closed 7/29/07)
* "Rent" 4721
* "Chicago" (Revival) 4474
* "The Lion King" 4106
"Miss Saigon" 4097
"42nd Street" 3486
"Grease" 3388
"Fiddler on the Roof" 3242
"Life With Father" 3224
"Tobacco Road" 3182
"Hello, Dolly!" 2844
"My Fair Lady" 2717
"The Producers" 2502 (closed 4/22/07)
* "Mamma Mia!" 2444
"Cabaret" (Revival) 2378
"Annie" 2377
"Man of La Mancha" 2328
"Abie's Irish Rose" 2327
"Oklahoma!" 2212
* "Hairspray" 2080
"Smokey Joe's Cafe" 2036
"Pippin" 1944
"South Pacific" 1925
"The Magic Show" 1920
"Aida" 1852
"Gemini" 1819
"Deathtrap" 1793
"Harvey" 1775
"Dancin'" 1774
"La Cage Aux Folles" 1761
"Hair" 1750
* "Avenue Q" 1692
"The Wiz" 1672
"Born Yesterday" 1642
"The Best Little Whorehouse in Texas" 1639
"Crazy for You" 1622
"Ain't Misbehavin'" 1604
* "Wicked" 1588
"Mary, Mary" 1572
"Evita" 1567
"The Voice of the Turtle" 1557
"Jekyll & Hyde" 1543
"Barefoot in the Park" 1530
"Brighton Beach Memoirs" 1530
"42nd Street" (Revival) 1524
"Dreamgirls" 1522
"Mame" 1508
"Grease!" (Revival) 1501
"Same Time, Next Year" 1453
"Arsenic and Old Lace" 1444
"The Sound of Music" 1443
"Me and My Girl" 1420
"How To Succeed in Business Without Really Trying" 1417
"Hellzapoppin" 1404
"The Music Man" 1375
"Funny Girl" 1348
"Mummenschanz" 1326
"Oh! Calcutta!" 1314
"Movin' Out" 1303
"Angel Street" 1295
"Lightnin'" 1291
"Promises, Promises" 1281
"The King and I" 1246
"Cactus Flower" 1234
"Sleuth" 1222
"Torch Song Trilogy" 1222
"1776" 1217
"Equus" 1209
"Sugar Babies" 1208
"Guys and Dolls" 1200
"Amadeus" 1181
"Cabaret" 1165
"Mister Roberts" 1157
"Annie Get Your Gun" 1147
"Guys and Dolls" (Revival) 1144
"The Seven Year Itch" 1141
"Bring in 'Da Noise, Bring in 'Da Funk" 1130
"Butterflies Are Free" 1128
"Pins and Needles" 1108
"Fosse" 1100
"Plaza Suite" 1097
"They're Playing Our Song" 1082
"Grand Hotel" 1077
"Kiss Me, Kate" 1070
"Don't Bother Me, I Can't Cope" 1065
"The Pajama Game" 1063
"Shenandoah" 1050
"Annie Get Your Gun" (Revival) 1046
"The Teahouse of the August Moon" 1027
"Damn Yankees" 1019
* "Monty Python's Spamalot" 1013
"Contact" 1010
"Never Too Late" 1007
"Big River" 1005
"The Will Rogers Follies" 983
"Any Wednesday" 982
"Sunset Boulevard" 977
"Urinetown" 965
"A Funny Thing Happened on the Way to the Forum" 964
"The Odd Couple" 964
* "The 25th Annual Putnam County Spelling Bee" 960
"Anna Lucasta" 957
"Kiss and Tell" 956
"Show Boat" (Revival) 951
"Dracula" (Revival) 925
"Bells Are Ringing" 924
"The Moon Is Blue" 924
"Beatlemania" 920
"Proof" 917
"The Elephant Man" 916
"Kiss of the Spider Woman" 906
"Thoroughly Modern Millie" 904
"Luv" 901
"The Who's Tommy" 900
"Chicago" 898
"Applause" 896
"Can-Can" 892
"Carousel" 890
"I'm Not Rappaport" 890
"Hats Off to Ice" 889
"Fanny" 888
"Children of a Lesser God" 887
"Kiss Me, Kate" (Revival) 885
"Follow the Girls" 882
"City of Angels" 878
"Camelot" 873
"I Love My Wife" 872
"The Bat" 867
"My Sister Eileen" 864
"No, No, Nanette" (Revival) 861
"Ragtime" 861
"Song of Norway" 860
"Chapter Two" 857
"A Streetcar Named Desire" 855
"Barnum" 854
"Comedy in Music" 849
"Raisin" 847
"Blood Brothers" 839
"You Can't Take It With You" 837
"La Plume de Ma Tante" 835
"Three Men on a Horse" 835
"The Subject Was Roses" 832
"Black and Blue" 824
"The King and I" (Revival) 807
"Inherit the Wind" 806
"Anything Goes" (Revival) 804
"Titanic" 804
From this article in Playbill News.
* "The Phantom of the Opera" 8157
"Cats" 7485
"Les Misérables" 6680
"A Chorus Line" 6137
"Oh! Calcutta!" (Revival) 5959
"Beauty and the Beast" 5461 (closed 7/29/07)
* "Rent" 4721
* "Chicago" (Revival) 4474
* "The Lion King" 4106
"Miss Saigon" 4097
"42nd Street" 3486
"Grease" 3388
"Fiddler on the Roof" 3242
"Life With Father" 3224
"Tobacco Road" 3182
"Hello, Dolly!" 2844
"My Fair Lady" 2717
"The Producers" 2502 (closed 4/22/07)
* "Mamma Mia!" 2444
"Cabaret" (Revival) 2378
"Annie" 2377
"Man of La Mancha" 2328
"Abie's Irish Rose" 2327
"Oklahoma!" 2212
* "Hairspray" 2080
"Smokey Joe's Cafe" 2036
"Pippin" 1944
"South Pacific" 1925
"The Magic Show" 1920
"Aida" 1852
"Gemini" 1819
"Deathtrap" 1793
"Harvey" 1775
"Dancin'" 1774
"La Cage Aux Folles" 1761
"Hair" 1750
* "Avenue Q" 1692
"The Wiz" 1672
"Born Yesterday" 1642
"The Best Little Whorehouse in Texas" 1639
"Crazy for You" 1622
"Ain't Misbehavin'" 1604
* "Wicked" 1588
"Mary, Mary" 1572
"Evita" 1567
"The Voice of the Turtle" 1557
"Jekyll & Hyde" 1543
"Barefoot in the Park" 1530
"Brighton Beach Memoirs" 1530
"42nd Street" (Revival) 1524
"Dreamgirls" 1522
"Mame" 1508
"Grease!" (Revival) 1501
"Same Time, Next Year" 1453
"Arsenic and Old Lace" 1444
"The Sound of Music" 1443
"Me and My Girl" 1420
"How To Succeed in Business Without Really Trying" 1417
"Hellzapoppin" 1404
"The Music Man" 1375
"Funny Girl" 1348
"Mummenschanz" 1326
"Oh! Calcutta!" 1314
"Movin' Out" 1303
"Angel Street" 1295
"Lightnin'" 1291
"Promises, Promises" 1281
"The King and I" 1246
"Cactus Flower" 1234
"Sleuth" 1222
"Torch Song Trilogy" 1222
"1776" 1217
"Equus" 1209
"Sugar Babies" 1208
"Guys and Dolls" 1200
"Amadeus" 1181
"Cabaret" 1165
"Mister Roberts" 1157
"Annie Get Your Gun" 1147
"Guys and Dolls" (Revival) 1144
"The Seven Year Itch" 1141
"Bring in 'Da Noise, Bring in 'Da Funk" 1130
"Butterflies Are Free" 1128
"Pins and Needles" 1108
"Fosse" 1100
"Plaza Suite" 1097
"They're Playing Our Song" 1082
"Grand Hotel" 1077
"Kiss Me, Kate" 1070
"Don't Bother Me, I Can't Cope" 1065
"The Pajama Game" 1063
"Shenandoah" 1050
"Annie Get Your Gun" (Revival) 1046
"The Teahouse of the August Moon" 1027
"Damn Yankees" 1019
* "Monty Python's Spamalot" 1013
"Contact" 1010
"Never Too Late" 1007
"Big River" 1005
"The Will Rogers Follies" 983
"Any Wednesday" 982
"Sunset Boulevard" 977
"Urinetown" 965
"A Funny Thing Happened on the Way to the Forum" 964
"The Odd Couple" 964
* "The 25th Annual Putnam County Spelling Bee" 960
"Anna Lucasta" 957
"Kiss and Tell" 956
"Show Boat" (Revival) 951
"Dracula" (Revival) 925
"Bells Are Ringing" 924
"The Moon Is Blue" 924
"Beatlemania" 920
"Proof" 917
"The Elephant Man" 916
"Kiss of the Spider Woman" 906
"Thoroughly Modern Millie" 904
"Luv" 901
"The Who's Tommy" 900
"Chicago" 898
"Applause" 896
"Can-Can" 892
"Carousel" 890
"I'm Not Rappaport" 890
"Hats Off to Ice" 889
"Fanny" 888
"Children of a Lesser God" 887
"Kiss Me, Kate" (Revival) 885
"Follow the Girls" 882
"City of Angels" 878
"Camelot" 873
"I Love My Wife" 872
"The Bat" 867
"My Sister Eileen" 864
"No, No, Nanette" (Revival) 861
"Ragtime" 861
"Song of Norway" 860
"Chapter Two" 857
"A Streetcar Named Desire" 855
"Barnum" 854
"Comedy in Music" 849
"Raisin" 847
"Blood Brothers" 839
"You Can't Take It With You" 837
"La Plume de Ma Tante" 835
"Three Men on a Horse" 835
"The Subject Was Roses" 832
"Black and Blue" 824
"The King and I" (Revival) 807
"Inherit the Wind" 806
"Anything Goes" (Revival) 804
"Titanic" 804
From this article in Playbill News.