Conaway, who had a history of addictions to drugs, alcohol and prescription painkillers, was hospitalised earlier this month after being found unconscious in his Los Angeles area home.
He was suffering from pneumonia and sepsis, and had been placed in a medically-induced coma.
The actor's family took him off life support on Thursday, media reports said.
A native of New York, Conaway began his acting career on Broadway but found national fame when he starred as Kenickie in the 1978 film musical "Grease," alongside John Travolta and Olivia Newton-John.
He also became a television regular for playing Wheeler, a cab driver, on the hit comedy "Taxi."
Conaway's problems with addiction were documented in 2008 when he appeared on the TV series "Celebrity Rehab".
