Ruta Lee, Marcia Wallace.

An obvious one is Richard Dawson who went from Hogan's Heros, to Match Game, to Host of Family Feud. Without the game shows, Dawson had little career.
Wally Cox on Hollywood Squares and really Peter Marshall whose major memory for most is the host of them.
George Goebel was a major one on Hollywood Squares. I once saw him live doing 90 minutes of stand up and believe me without tv and games he would not be remembered.
A Smile is priceless and Can Be Addicting

Orson Bean, Jaye P. Morgan, Henry Morgan (no relation to Jaye P.).

Cliff Arquette (Charlie Weaver)

Brett Somers, Charles Nelson Reilly, Fannie Flagg, Richard Dawson (he was a regular on Match Game before getting the hosting job on Family Feud).
Nipsey Russell
I don't know what they have to say. It makes no difference anyway. Whatever it is, I'm against it.

Unfortunately, I read that only one complete episode and one partial episode survives of that series. Producer Bob Stewart did not begin regularly keeping the tapes of the shows he produced until around 1977/1978.
Have you played Atari today?

My brother-in-law's dad was on Eye Guess. Embarrassingly giddy, but he won.
"I was so disappointed when they closed the Stock Exchange." - Donald Trump, 9/11/2001

Bill Cullen appeared as host on more game shows than anybody else, often hosting several shows at the same time, AND still found time to be a guest celebrity on others. There were at least two shows where Cullen both hosted and appeared as guest celebrity (For example, he hosted the syndicated version of "Pyramid" and appeared as celebrity guest on the daytime version. He also appeared as both substitute host on "Password Plus" and a celebrity guest on "Super Password").
Have you played Atari today?

Bill Cullen, Kitty Carlisle (though she was in Night at the Opera)
"I was so disappointed when they closed the Stock Exchange." - Donald Trump, 9/11/2001

Jm J Bullock also appeared on over 20 episodes of
Body Language (1984)
, a show I've been needing to check out (well, it's a Mark Goodson Production, which is always a good sign). The shows cast list seems to include a lot of professional game show celebrities (Betty White, Charles Nelson Reilly, Tom Poston, Jo Anne Worley, etc.)
Have you played Atari today?

Jm J Bullock also turned into a 'Hollywood Squares' celeb, in the 80s & 90s.

• What are you gonna do, when the world catches on?

Paul Lynde with
The Hollywood Squares
is the very definition of this. Although Lynde had had a long-running career in stage, film, and television it's my bet that audiences of a certain generation knew him more from his appearances on that show than from anything else he'd ever done.
50 Is The New Cutoff Age.