Miyazaki/Studio Ghibli For Younger Kids:
- My Neighbor Totoro
- Ponyo
- Spirited Away
- The Secret World of Arietty
- Kiki's Delivery Service
- Pom Poko
For maybe when they're getting older?
- Howl's Moving Castle
- The Wind Risees
- Castle In The Sky
- Princess Mononoke
- Nausicaä of the Valley of the Wind
Some other decent ones for kids of various ages:
Animated/Claymation
Series:
- Adventures of Sonic the Hedgehog
- Alvin & The Chipmunks
- Captain Planet and the Planeteers
- Ducktales
- Gumby
- Inspector Gadget
- Rugrats
- Rescue Rangers
- Scooby Doo
- Yogi Bear
Movies:
- Alice in Wonderland
- All Dogs go to Heaven
- An American Tail
- An American Tail: Fivel Goes West
- The Black Cauldron
- Charlotte's Web
- FernGully
- James and the Giant Peach
- The Land Before Time
- The Nightmare Before Christmas
- Peter Pan
- Pinochio
- RobinHood
- The Rescuers
- The Rescuers Down Under
- The Secret of NIMH
- The Sword in the Stone
- Thumbelina
- Wallace and Gromit (All of them are great)
Live Action Series:
- Bill Nye The Science Guy
- Beakmans World
Movies:
- Beetlejuice
- Casper
- Ernest Goes to School (and all the other ones really)
- Honey I Shrunk The Kids
- Hook
- Jumanji
- E.T.
- Edward Scissor Hands
- Flubber
- Ghost Busters
- The Goonies
- Labyrinth (Creepier vibe than I remember)
- The Little Rascals
- Mary Poppins
- Mr. Mom
- Mrs. Doubtfire
- The Never Ending Story
- Operation Dumbo Drop
- Patch Adams
- Sandlot
- Short Circuit
- Space Jam
- Toys
- Tron
- We're back a dinosaur story
- Who Framed Roger Rabbit (Animated and Live Action)
Edit: awful formatting... And typos