Although it was not as popular as Rugrats, Klasky Csupo's The Wild Thornberrys was a great cartoon that ran for a good six years (and reran until a few years back). It follows the titular Thornberrys as they travel the world filming wild animals. The protagonist of the show, Eliza, is a nerdy yet very brave girl with the ability to speak to animals. Perhaps I liked this because I always wished that I could speak to animals, but it provided some pretty interesting episodes and taught some good lessons.
Like other Nickelodeon cartoons, it wasn't always what you would expect kids to be watching (feral son, parents that let their children climb mountains unattended, lots of conflicts with poachers), but it was a thoughtful and interesting series. The animation was what you expected from Klasky Csupo and the stylized look was one familiar to kids at the time. Give a few episodes a try and you might become a fan. There is even a movie!
Image via sodahead.com