A few of the names were predictable. Ken Jennings, the “Jeopardy!” champion who holds the longest winning streak on the show, would be the ideal choice, some fans said.
Other suggestions were more unusual. What about Rosie Perez, the charismatic actress who, in “White Men Can’t Jump,” played a trivia geek who was determined to get on the game show?
As fans mourned the longtime “Jeopardy!” host Alex Trebek, who died at 80 on Sunday, they also began to speculate about who might replace him. Social media buzzed with suggestions and jokes about who should host the show, from mainstream options, like Mr. Jennings and the ABC News anchor George Stephanopoulos, to more jarring ones, like the brash comedian and podcast host Joe Rogan.
Heated debates around the replacement of a popular game show host are hardly new. Reddit, the social networking and message board site, is rife with rankings and discussions of who was the best host of “Family Feud.” When Bob Barker retired from the “The Price is Right” in 2007 after 35 years and 6,828 episodes, fans speculated anxiously about who would replace him.
Mr. Trebek was not even the first host of “Jeopardy!” When the show was revived in 1984, some fans of its original host, Art Fleming, bristled at the cerebral Mr. Trebek, who was not afraid to show off his knowledge of trivia, said Claire McNear, whose book about “Jeopardy!,” “Answers in the Form of Questions,” was released on Tuesday.
Now, he is synonymous with the show.
“Trebek really felt like a member of the family because he was there in your living room every night,” Ms. McNear said.
It was understandable, then, that fans would ponder Mr. Trebek’s replacement even as they grieved him, she said.
So, at least according to the fans, who are the contenders?
Many fans on social media were pushing for LeVar Burton, who hosted “Reading Rainbow”; played Lt. Geordi La Forge, the brainy, blind engineer on “Star Trek: The Next Generation”; and portrayed Kunta Kinte in the 1977 mini-series “Roots.”
By Tuesday, more than 1,500 people had signed a petition urging Sony Pictures Entertainment Inc. and the show’s executive producer,