I can't say I watched all that many cartoons. I was very into Wheel of Fortune as a youngster and in fact still watch the show on a regular basis. I actually got to see a live taping of the show in 1998, and saw the set when I visited Disney World in 1989!
For me, the best childhood show is and always will be Mr. Rogers. I'm from Pittsburgh, PA, which is his hometown, and I have met the show's guitarist, Joe Negri. He's actually a professor of music at Duquesne University, which is in Pittsburgh and is not too far from the Mellon Arena where the Pittsburgh Penguins play. Mr. Rogers would always manage to teach a lesson and make me feel good about myself. When I went off to college, my grandmother bought me a book called "Life According to Mr. Rogers". It's a great read.
I know a lot of people my age (I will be 20 in September) bash Mr. Rogers because the show doesn't have the violence and whatnot found in other cartoons like Bat Man, but you will never find a better children's show. As a future elementary school teacher, it always helps to remember what filled you with humanity as a child.
And yes, I did take heat for not watching the same shows as a lot of people. I found some books at the library and read them with the intent of finding out what these other shows were about, but I could not coerce myself to like them. I think it's because I was so used to Mr. Rogers.
There were two other excellent shows on PBS that I watched in elementary school. One was called "Square One" and it was a very entertaining show that taught mathematics behind the scenes. It featured some great segments such as Mathnet Detective Agency, Math-Man the Pacman clone, and my personal favorite, the music videos. One song that I particularly loved was called "Less than Zero". The lyrics went "Less than zero, he's an empty hero...I'm just a negative guy!" So entertaining yet so subliminally educational.
I also used to watch the original Carmen Sandiego show. While my intent was not to learn some geography, I picked a lot of it up anyway. I liked to watch it because of the show's singing group, Rockapella. I own two Rockapella albums and played one all the way to Duluth on a 1993 vacation! I also had the computer game for my Macintosh, but I usually needed the desk encyclopedia that came with it to win (until I hit middle school).
If you truly want a good animated cartoon, however, I would go with the old Mickey Mouse shorts from the 1930s. They're not as "kiddy" as the modern Mickey Mouse and are actually quite funny. You can find them on DVD these days. When your grandparents were teenagers, they would show this at the theater before the movie and they would sometimes be more entertained by the cartoon shorts than the movies themselves! The old Pink Panther series were usually good too.