I don't think there are too many people still living who grew up without television. I think everyone can relate to watching their favorite cartoons on Saturday mornings. This list includes all the cartoons that were part of my childhood. I excluded cartoons that were old re-runs as they were not new when my generation saw them.
5. Hey Arnold
Hey Arnold was one of my favorites on Nickelodeon. It was about a young kid named Arnold who lived with his wacky grandparents in their boarding home. I think the thing I remember most was Helga Pataki as she was often the source of Arnold's misery. Ironically she had the biggest crush on him, stupid kids.
4. Dexter's Laboratory
This was arguably Cartoon Network's finest cartoon. The show was about Dexter, the self-described boy genius. Which was pretty true as he was smart enough to have a hi-tech lab in his house without his parents knowing. But not smart enough to know how to keep his goofy sister out of it or keep her from breaking his equipment.
3. Rocko's Modern Life
Rocko's Modern Life was easily the most creative cartoon I've ever seen. It had a lot of smart humor, including innuendos I never got when I was younger. It's rather strange this show only lasted three years before they stopped making episodes. But that was a common thing with cartoons.
2. Spongebob Squarepants
Spongebob came out in 1999 when I was in 5th grade I think. It's amazingly still going, but for as good as it is, it shouldn't be that surprisingly. The cast of characters are just genius. There's no fictional character quite like Spongebob, or his dimwitted starfish pal Patrick, or their cynical neighbor Squidward.
I think one of the reasons I loved Rugrats so much was that it was always around and relevant through my whole childhood. It also focused a lot on growing up so there was a lot to relate to. I thought all the characters and their families were really unique. I also liked how they clashed against the "evil" Angelica who was Tommy's cousin. I think everyone had that slightly older relative we despised in childhood.