I am an animation fan, and have watched quite a number of shows.
My Little Pony: Friendship is Magic
I highly recommend My Little Pony: Friendship is Magic. It's on Netflix. The art is absolutely beautiful, and the stories are fun and carry a great message about... Friendship. I see this show as an example of how we reflect God's grace and creativity through the arts.
Veggie Tales
I was introduced to Veggie Tales by a Christian Vegeterian. I thought, "oh, man, what kind of propoganda is this??" I went from total cynicism to being as enthralled as my kids in about 5 minutes. I recommend going from oldest to newer. Song of the Cucumber and The Pirates who Don't Do Anything kill me every time.
Barbie Movies
If your child likes Barbie, there are a number of Barbie movies that are absolutely great... No, I'm not kidding... Yes, they really are great! They focus on introducing kids to the fine arts, and they're tremendously successful at meeting this goal.
The first was made in 2001, Barbie in the Nutcracker. It uses Tchaikovsky's score and tells a very affirming story about strength and love. The special features on the DVD make this a knock out. There's a documentary on Juliard, focusing on a couple of the children in the ballet program. Not only does this connect to the ballet elements in the movie, but also shows real children really working on becoming ballerinas. I wish every Children's DVD was this thoughtfully compiled.
Barbie Swan Lake from 2003 connects to painting, and the special features follow a young adult as she prepares for her first art show.
Barbie Princess and the Pauper focuses on song.
Barbie and the Magic of Pegasus from 2005 incorporates Beethoven's 6th Symphony.
Yes, each of these had Barbie toys available, which clouded many a review. But the producers of these films really wanted to create something of quality, and they did so with beauty and grace.
After these first four, the movies started becoming hit and miss. (Be warned, do NOT tread into Barbie and the Dream House, as this series contains just about every horrible Barbie cliche you can possibly imagine. It's done this way on purpose, but kids don't realize that, so it inadvertently glorifies the shallowest aspects of the characters.)
Steven Universe [EDIT: Oops. This show is too mature for a 4 year old.]
I also will go out on a limb and recommend Steven Universe. But only if you watch it with your kids. It involves aliens from a planet of all females, so it has gay overtones. But far more importantly, it also illustrates unconditional love through the main character, even in situations where relationships can be difficult and complicated. Another show where I see the Grace of God manifested, regardless of -- or in spite of -- Christian views on homosexuality.
-Pie