Muppet Babies definitely started a trend. I totally loved The Flinstone Kids!!! (They had the great Captain Caveman and Son segments!!!) I also loved Tom and Jerry Kids, which was hysterical. The Droopy segments were always great too. And A Pup Named Scooby Doo rules!!! That is incredibly funny and I loved the dance segments, the music, and Scooby not getting Shaggy's jokes. There's still lines I quote from the show today and my brother and I laugh at it.
"Why do you keep calling me 'Raggy'"? - Shaggy to Scooby, after losing his memory and thinking he's Commander Cool
Nowadays, there's also Baby Looney Tunes, which even I'll admit is just kind of okay, but not quite as good as the adult counterparts. You could even count X-Men Evolution as another cartoon inspired by Muppet Babies. Because the whole thing of the X-Men growing up together at Professor X's School for the Gifted just didn't happen in the comics. As far as I know, they were already adults when they were recruited. True, some teenagers like Kitty Pryde were there and that would be okay. But even though there are some issues like that, I still like the series because it really works.
I'm sure there's even more examples I'm forgetting. Like "Young Hercules", the live action Fox Kids version of Kevin Sorbo's "Hercules". Or "The New Archies"- the great late 80s cartoon that had all the Archie Comics gang as middle schoolers. Archie, Jughead, Reggie, Betty, Veronica, Mr. Lodge, Mr. Weatherbee, Ms. Grundy, Moose and Hot Dog were all there. For some reason, Dilton and Chuck Clayton weren't. However, there was a black boy who was smart like Dilton called Eugene that was on the show whose girlfriend was Nancy. So they more or less combined Chuck and Dilton to create Eugene. (Bascially, have the token black character there. But he did have an important role on the series and was one of the gang, so he wasn't totally a "token black character". Anyway...)
Of course, I can't forget one of my favorite series based on one of my favorite movies. "The Young Indiana Jones Chronicles" gave us the adventures of Indiana Jones as a kid, teenager, and young adult. (Not to mention a 93 year old grandfather!) Very cool show.
Believe me, I'm sure there's other examples too.
The list goes on.