The show you are thinking of was Hanna Barbara's Laff Olympics. One of their vehicle shows to get as much milage out of their anthropomorphic animal characters as possible. Another was the ahead-of-its-time-and-probably-banned-like-Doctor-Seuss'-"The-Lorax" enviromentally-themed Yogi's Ark. I would love to see some of those as I was formulating a story about how the envormental message was just a cover, the real story was about how all of the animals were really just trying to escape human opression (from Mr. Peebles, Park Ranger Smith, Major Minor, and others).
I did grow up in the days when Saturday Morning was king and the networks really courted the kids with the new seasons. There was a period of a few years when the networks would even air prime-time "preview" shows about a week before the new line-up of Saturday morning shows were to air. One was even hosted by Leonard Nimoy! (Imagine the horror of Nemoy talk-singing "Come Saturday Morning" with a chorus of chirpy kids!) And you usually had heavy advertizing in comic books of the shows that would soon grace your Saturday morning. Though I couldn't stand it after the first 12 years, Scooby Doo had to be the undisputed king of Saturday morning, managing to be reinvinted every few years ad nauseum. But my favorites were Jonny Quest (the single best show ever) and the more mature, continuing series shows like Valley of the Dinosaurs (an animated competitor of the live action Land of the Lost), Sea Lab 2020 (a show that it took years for me to prove even existed, which has recently been given hillarious new life on Cartoon Network's "Adult Swim" block of programing as the recut and redialoged Sealab 2021, with outrageous new scripting in the vein of Space Ghost Coast to Coast), The Herculoids, and others. Of course during that time the live action boom was in full swing with Land of the Lost, The Lost Saucer, The Far Out Space Nuts, The Ghostbusters (featuring monser make-up legend Rick Baker as Tracy the Gorilla), Doctor Shrinker, Sigmund and the Sea Monsters and others, including an amalgam of the two, Uncle Croc's Block, a short-lived live-action showcase for various cartoons hosted by Charles Nelson Reily in a crocodile suit! I believe that Hanna Barbara introduced Captain Caveman on this show before spinning him off on his own.