Darrin Stevens(Dick York) and Kelly Bundy come to mind.
I recall seeing someone else do it too, but forgot who.

Private Frank Pike (Ian Lavender) Dad's Army

Poor Darrin probably only did it 'cause he was under Endora's spell.

Bud Bundy in his regressive state, i.e. his juvenile pajamas, a while after his near-death experience of an arrow shooting an apple above his head.

There was a Happy Days episode when Richie Cunningham sucked his thumb after Howard and Marion wouldn't let him have a motorcycle. He did get one and had an accident that put him in a coma. The memorable scene was in the hospital and Fonzie cried.

Herman Munster (Fred Gwynne) - briefly with his old baby rattle & bonnet, and I think he may have gone for the thumb in that scene.

Private Frank Pike (Ian Lavender) Dad's Army
never heard of the show; is it on Netflix or something?

There was an episode of Benson where Clayton was either seen sucking his thumb or it was just mentioned. I don't remember which.

never heard of the show; is it on Netflix or something?

It is on Netflix, that's where I've been watching it. It's a British sitcom from the late 60's/70's. Set during WWII, about a group of volunteers serving as home guard to help protect England.

Very funny.