A&E (Arts & Entertainment Network)
(launched in 1984)
IMDb; official website; TV Tropes; Wikipedia

Biography (1987 - 2006; Biography Channel 2006 - 2012)
Poirot (1989-2013 on ITV; I'm not sure when or how much of this I saw on A&E. Also aired on PBS)
P.T. Barnum (9/12-13/1999; miniseries)
A Nero Wolfe Mystery (4/22/2001 - 8/18/2002)
Benedict Arnold: A Question of Honor 1/13/2003; TV movie)
Karroll's Christmas (12/14/2004; TV movie)
Bates Motel (3/18/2013 - 4/24/2017; I've only seen the first season)
Roots (5/30/2016 - 6/2/2016; miniseries; also aired on History / Lifetime / LMN)