Bain, who starred opposite a young Gary Coleman in the show, died in California of natural causes, his daughter said.
The comedy, which played on the contrasting lifestyles of rich white and poor black communities in the US, was seen as groundbreaking in the 70s.
It ran for eight seasons, over six years, coming to an end in 1986.
Its success was largely attributed to the play-off between the mischievous young Arnold (played by Coleman) and Bain’s character, Phillip Drummond, a rich, widowed industrialist who takes in the two young sons of his housekeeper after she dies.
Coleman’s oft-repeated line to his brother, “What you talkin’ ’bout, Willis?” became a catchphrase of the era.
The younger stars of the show were later caught up in controversy, with Coleman dying following a brain haemorrhage at the age of 42, after years of financial and legal woes.
Co-star Dana Plato, who played Drummond’s daughter in the show, died in 1999 after an apparent drug overdose, while Todd Bridges, who played Coleman’s elder brother in the show, revealed that years of childhood abuse led to drug addiction.
“It’s painful,” Bain once told a journalist. “It is really painful. It leaves you with such a helpless feeling. I can’t bear the thought. I love them all.”
Bridges, who eventually conquered his addiction, told a magazine that Bain had become like a real father to him.
Bain would revive his character for a one-off episode of the 1990s sitcom The Fresh Prince of Bel-Air, starring Will Smith – whose storyline, about a rapper from the mean streets of Philadelphia who moves into a life of luxury in California, in many ways echoed the earlier show.
Success for the Canadian-born actor began on the stage and daytime television – notably in the cult vampire drama Dark Shadows – recently made into film by Tim Burton, starring Johnny Depp.
His first prime-time role was opposite The Golden Girls’ Bea Arthur in Maude (1972-78), playing an uptight physician. The success of the show led to his casting in Diff’rent Strokes.
After becoming a household name in the 1980s, Bain starred in the short-lived political comedy Mr President, and returned frequently to the stage throughout his career, last appearing on Broadway in 1992.
He is survived by his daughter, Jennifer, and two sons, Mark and Kent. His wife Monica died in 1999.