Whatever decade you grew up in, you'll probably have fond memories of the morning and Saturday cartoons that you watched. For me, it was the eighties, and cartoon series like: Ulysses, Thundercats, Transformers, and The Lost Cities of Gold.
My favourite crtoon from the 80s is The New Adventures of Winnie The Pooh. It ran from 1988 to 1991. For a show that was entirely in the 80s, then it would be Captain Caveman and Kid or The Flintstone Kids, which both ran between 1986-1988.