Conaway was taken off life support at Encino Hospital Medical Center, said his sister Carla Shreve. He had pneumonia when he arrived unconscious at the hospital May 10, the result of "just too many prescribed drugs," and was placed in a medically induced coma, she said.
Conaway played Kenickie, the Rydell High School pal of Travolta's Danny Zuko.
"I got so many hickeys, people will think I'm a leper," Stockard Channing's Rizzo tells Kenickie at one point, examining her neck in a compact mirror.
"Cheer up," Conaway's character memorably replies. "Hickeys from Kenickie is like a Hallmark card."
Later the same year, Conaway began playing Bobby Wheeler, the cab-driving struggling actor in "Taxi."
The series about a group of New York cabbies, whose ensemble cast included Judd Hirsch, Danny De Vito, Marilu Henner and Tony Danza, ran until 1983.
Although the show gave Conaway continued national exposure, he broke his contract and quit after three seasons, having reportedly grown tired of being typecast as a "blond bimbo" and the butt of struggling-actor jokes.
"In 'Taxi,' I kept doing the same scene for three years," he told the Toronto Star in 1989. "I was underused. It's natural when there are seven people involved in a half-hour show."
In a 1985 Associated Press interview, he said that he had become "very depressed" while doing the series.
"Hollywood can be a terrible place when you're depressed. The pits," he said. "I decided to change my life and do different things."
His various projects, however, did little to further his career.
He returned to series TV in 1984, starring as Prince Erik Greystone on "Wizards and Warriors," a fantasy adventure series that ended after eight episodes. Then came a role on "Berrenger's," a short-lived 1985 nighttime soap opera.
The same year, Conaway was on Broadway in "The News," a rock musical about New York City tabloid journalism that closed after two days.
He later appeared in the soap opera "The Bold and the Beautiful" and the 1990s sci-fi TV series "Babylon 5." TV guest shots and roles in films and TV movies followed, as did stories of his substance abuse.
Conaway already was known for leaving VH1's "Celebrity Fit Club" for a rehab attempt in 2006 when he joined eight other celebrities on the premiere of VH1's "Celebrity Rehab With Dr. Drew" in 2008.
He was so intoxicated the morning he checked in that subtitles were required to translate his slurred speech.
"Celebrity Rehab With Dr. Drew" added a new dimension to Conaway's faded celebrity.