There have been some—Steve Martin and Tim Allen spring to mind—who started out as stand-up comedians but went on to a very successful acting career, with a variety of roles—but all or mostly all in comedies, as far as I can remember.
John Goodman. I finally got a Blu-Ray of Matinee , from 1993. It’s a comedy, but since it’s set in the Florida Keys during the Cuban Missile Crisis, it’s somewhat of a dark comedy. Goodman’s character is an avatar of William Castle , and there are two layers to it, the way he plays it. On the surface, he’s a showman, a genial host with contagious enthusiasm. Underneath that, though, he’s super-practical and calculating. There’s a bit late in the film when a movie theater will have to be evacuated, but a panicked stampede will be just as bad as if they’d stayed there. The main kid says “Turn off the projector!”
“No. Then they stomp.” You’d have to hear it, but his tone is exactly what I’ve heard from directors, show runners, department heads…anyone who has a lot of responsibilities but never loses his cool. It would have be so easy to play the character simply as a buffoon, but JG was subtle, and created a “round” character.
Wasn’t Tom Hanks initially known as a sitcom actor? E. g., “Bosom Buddies.”
A sitcom actor and an actor in sex comedy movies like “Bachelor Party”
Jim Carrey did very good work in The Truman Show
This is a pretty good little docu-drama involving Keenan Wynn and the casting of his father Ed Wynn in a live dramatic role, and his fear that his father will revert to his old vaudville schtick. “The Man in the Funny Suit” He ends up nailing it.
And Eternal Sunshine of the Spotless Mind was excellent.
Woody Harrelson in The People vs. Larry Flint
Sacha Baron Cohen of Borat and Ali G fame is amazing in his serious roles. The Spy on Netflix in particular was a fantastic performance.
I’m thinking that in general comics do better with serious than actors of serious roles do with comedy.
Inthe other direction I got Leslie Nielsen but no one else pops right into mind.
Jerry Lewis also played a dramatic role in the tv series “Wiseguy” in the 1980s (unusually, this series had “arcs” - the main character would go undercover for several episodes at a time, so Lewis played the villain for several episodes)
It’s so weird to see him up goofing it up on the stage in “Scarface.”
Damon Wayans has been good in some more serious stuff. Mostly action, but Bamboozled, for instance, while dark comedy, also had quite serious bits.
You underestimate the popularity of Quincy, M.E. 
As someone that’s never watched L&O or CSI or most of those shows, seeing him in the commercials gives me the same reaction as seeing Ice T in those commercials. It’s sort of jarring in a ‘why is he on that show?’ way.
Plus, for whatever reason, when I hear ‘Richard Belzer’, I picture Richard Lewis (and I always picture him in the Boku commercials trying to get grownups to buy juice boxes).
How about a future one…If she sticks with it long enough, in 10 or 20 years we’ll have a generation of new Jeopardy! viewers finding out that Miyim Bialik was in multiple, hugely popular comedy sitcoms (and the lead in one).
Charles “Chip” Esten (best known for his improv comedy on “Whose Line Is It Anyway”) has done some convincing dramatic acting, including a recurring role on “Big Love.”
Olivia Colman raises the bar far above “good” acting skills.
She had a very famous comedy career until shifting more towards dramatic roles and has never looked back.
She’s a guarantee of quality in whatever she’s in and though she did eventually win an oscar how she was never even nominated for “Tyrannosaur” baffles me to this day.
A lot of great answers here! I knew I was drawing a blank on a lot of examples.
Ugh, I hope she doesn’t stick with it. She was among my least favorite of the guest hosts, especially knowing of the controversial stance she’s taken on vaxxing in the past. Seems like a bad choice for someone like that to host a game show that values facts and knowledge. Is she full-timing it now, or just part-time still?
If we’re going with Wayans brothers, Marlon Wayans is fantastic. Like Adam Sandler, he seems to prefer making terrible broad comedies, but his dramatic chops are sharp. Most recently in the Aretha Franklin movie.
Robin Williams was an amazing stand-up comic, as well as a comic actor, but he took on quite a few dramatic roles, and did well enough at them to get three Oscar nominations, winning one of them (for Good Will Hunting).
That’s why I was trying to phrase it as ‘if she sticks with it’ as opposed to ‘if she/the network ride out the backlash’.
No idea. I watched one episode a while ago just to see it. But other than Alex’s final show, I haven’t watched a single episode (much less watched it regularly) for years.