ISHPEMING, Mich.—On Sunday, Carl Pellonpaa is marking the end of an era in television history with two words: “siinä kaikki”—that’s it.

After 53 years and more than 2,650 straight weekly episodes of hosting “Finland Calling,” Mr. Pellonpaa will cap a career that far outpaces David Letterman, Johnny Carson and “Saturday Night Live.” Some might say he is Finnished.

Mr....