Below are some YouTube videos for kids (I haven’t viewed every last one of these, but they look OK–you might want to view them before showing them).
Here are some YouTube pages containing videos of Peep and the Big Wide World (Wikipedia provides some background):
tinyurl.com/PeepBWW1
tinyurl.com/PeepBWW2
tinyurl.com/PeepBWW3
tinyurl.com/PeepBWW4
I’ve only looked at a couple of Charlie and Lola animations, but they look interesting (again, Wikipedia gives some background). Here are some of them on a page:
tinyurl.com/LolaCharlie
Here are some Weston Woods and/or Scholastic animations based on children’s storybooks:
Tomie dePaola:
Charlie Needs a New Cloak
youtube.com/watch?v=A16Hv6Gx41M
Strega Nona
youtube.com/watch?v=0bQCYw0ehVo
Eric Carle:
The Very Hungry Caterpillar
youtube.com/watch?v=HpISHA8Fs4w
Papa, Please Get the Moon for Me
youtube.com/watch?v=9Oy8u8W0_do
The Very Quiet Cricket
youtube.com/watch?v=daGNjc2OfOk
The Mixed-Up Chameleon
youtube.com/watch?v=FNolRgH7AIU
Steven Kellogg, The Mysterious Tadpole
youtube.com/watch?v=4jTUg370sQk
Tomi Ungerer (these might be a little edgy for kids’ stories):
The Three Robbers
youtube.com/watch?v=0j8AYWIiZ5Y
Moon Man
youtube.com/watch?v=DljyC2r9rNA
The Hat
youtube.com/watch?v=wG9kQH1lcdo
The Beast of Monsieur Racine
youtube.com/watch?v=JHBZb-WlXZE
Gene Zion, Harry, the Dirty Dog
youtube.com/watch?v=wrrgNEGiDbE
Crockett Johnson, Harold and the Purple Crayon (be forewarned if you’re showing this video to kids: the username FeministWhore is situated directly above the video)
youtube.com/watch?v=NzaovPWUb-0
Jenny Wagner and Ron Brooks, John Brown, Rose, and the Midnight Cat
youtube.com/watch?v=l8rOvHJf98I
James Cressey, Fourteen Rats and a Ratcatcher
youtube.com/watch?v=MHOQ-XX1JYw
Pat Hutchins, Rosie’s Walk (Rosie the hen calmly strolls across the yard, around the pond, over the haystack, past the mill, etc., as the not-so-wily fox tries and fails to catch her.) youtube.com/watch?v=pIQDo0n4mLk
A song, apparently by Rose Bonne and Alan Mills, “There Was an Old Lady Who Swallowed a Fly,” performed in a Weston Woods animation by Simms Taback:
youtube.com/watch?v=altckbVlceM
I think there are also some animated Dr. Seuss books on YouTube, and some other animated storybooks.