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The all-time list for late night show runs:

David Letterman - 43 years (Late Night 1982-93, Late Show 1993-2015)
Johnny Carson - 30 years (Tonight Show 1962-92)
Conan O'Brien - 28 years (Late Night 1993-2009, Tonight Show 2009-10, Conan 2010-21)
Jimmy Kimmel - 23 years (Jimmy Kimmel Live 2003-2026)
Jay Leno - 22 years (Tonight Show 1992-2009, Jay Leno Show 2009, Tonight Show 2010-14)
Stephen Colbert - 20 years (Colbert Report 2005-2014, Late Show 2015-2026)
Jon Stewart - 17 years (Jon Stewart Show 1993-95, Daily Show 1999-2014)
Carson Daly - 17* years (Last Call 2002-2019, though it stopped being a talk show in 2009)
Jimmy Fallon - 15+ years (Late Night 2009-14, Tonight Show 2014-present; is booked to host until 2028)
Tom Snyder - 12 years (Tomorrow 1973-81, Late Late Show 1995-1999)
Seth Meyers - 11+ years (Late Night 2014-present; is booked to host until 2028)
Craig Ferguson - 9 years (Late Late Show 2005-2014)
Bill Maher - 9 years (Politically Incorrect, 1993-2002)
James Corden - 8 years (Late Late Show 2015-23)
Craig Kilborn - 7 years (Daily Show 1996-98, Late Late Show 1999-2004)
Trevor Noah - 7 years (Daily Show 2015-22)
Arsenio Hall - 6 years (Arsenio Hall Show 1989-94, 2013-14)
Bob Costas - 6 years (Later, 1988-94)
Jack Paar - 5 years (Tonight Show 1957-62)
Steve Allen - 3 years (Tonight Show 1954-57)
Greg Kinnear - 2 years (Later, 1994-96)
Lilly Singh - 2 years (A Little Late 2019-21)
George Lopez - 2 years (Lopez Tonight, 2009-11)
Cynthia Garrett - 1 year (Later, 2000-2001)
Joan Rivers - 1 year (The Late Show 1986-87)
Pat Sajak - 1 year (The Pat Sajak Show, 1989-90)
Sinbad - 7 months (Vibe 1997-98)
Keenan Ivory Wayans - 7 months (Keenan Ivory Wayans Show 1997-98)
Wanda Sykes - 6 months (Wanda Sykes Show 2009-10)
Magic Johnson - 3 months (The Magic Hour, 1998)
Chris Spencer - 2 months (Vibe, 1997)
Chevy Chase - 1 month (The Chevy Chase Show, 1993)

That's all I can think of. Johnny Carson's 30 year run on a single show will never be topped, though Kimmel came close