Some time back I was looking up on Saturday Morning Supercade and came across this website:
You might get a kick out of the site, although it's a mess in terms of organization. I think it was that site where I'd read that trends against advertisement in cartoons was a large factor in the decline of the Saturday Morning lineup in the late-80s. I'd read somewhere else that college football had also started airing toward the end of the "golden age" of Saturday morning cartoons.
As jolanar also points out, I think there is currently a resurgence of programing on during Saturday morning. It's still not a prolific as it was from the 60s-80s. I don't get that same feeling where all the networks are competing with their cartoon lineups, like it was back then.
You should get a kick out of this silentasylum: we use a streaming media box in our home and I made a "Super Saturday Morning Playlist" for our kids to watch when they get up before us, which is usual for Saturday mornings (although I'm getting home from work a bit later in the morning...) It's a "smart playlist" based on shows not recently watched. It's a mix of old and new shows that I know our kids like, and among them: Pee-Wee's Playhouse, Transformers G1, Adventure Time, Regular Show, Spongebob, many more, but yes - also Muppet Babies.
As for my favorites from the time, I really remember the above-mentioned Saturday Morning Supercade, Snorks, Smurfs... there was a game show I used to watch based around arcade games. A bit later on I remembered watching Pee-Wee and then Hey Vern, It's Ernest!. Earlier in my time, there was the Superfriends Hour (which I also have on the playlist for my kids). At some point, even earlier, I remember the Rocky and Bullwinkle Show being a pretty regular occurrence.
Okay, okay, I went to the site I posted above and had a total recall moment - Godzilla, Dugeons and Dragons, Mr. T's Show, Alvin and the Chipmunks, Kidd Video (live action), The Amazing Spiderman, The Littles, ...
I'm drowning in nostalgia and could go on forever with these shows I remember. I had a lot of favorites.