Here's a list of movies with attractions for each park. I didn't include Meet & Greets or Character Meals, only rides and shows. I wrote watch beside the ones that seemed to help explain an attraction better.
You will probably find your kids have already seen a number of these movies to begin with, and as others have stated, if you don't plan on experiencing a particular attraction, no point watching the movie.
Also, some of the attractions pretty much just retell the story, so not sure if you would want to watch those before going or not. Some of the rides also stand fine alone with no knowledge of the movies, like Dumbo, Aladdin's Carpets, the Tea-Cups, and the Nemo ride at Epcot, so totally up to you if it is important to you to understand those movie references or not. It's still fun to spin around or look at the aquarium either way.
Magic Kingdom:
Toy Story
Dumbo
Beauty and the Beast (attraction reenacts movie)
Haunted Mansion - watch, unless they scare easy, it is a comedy
Alice and Wonderland
Aladdin
Winnie the Pooh (attraction reenacts movie)
Monsters Inc. - watch
Peter Pan
Pirates of the Caribbean - watch, except OP's kids probably a little too young
Snow White
Song of the South - watch, makes the ride make more sense to at least watch the tar baby cartoon part, but good luck finding the banned movie
Country Bears
Lilo & Stitch
Swiss Family Robinson - watch
Tom Sawyer - watch
Little Mermaid (attraction reenacts movie)
Epcot:
Phineas & Ferb tv show - watch
The Three Caballeros
Finding Nemo
Hollywood Studios:
Honey I Shrunk the Kids - watch
Pirates of the Caribbean
Any Muppet movie - watch
Star Wars - watch
Toy Story - watch
Tower of Terror - watch, unless scare easy, was a Disney channel made for TV movie so pretty tame, but still some intense scenes
American Idol tv show (attraction reenacts movie)
Beauty and the Beast (attraction reenacts movie)
Little Mermaid (attraction reenacts movie)
Indiana Jones - watch
Cars / Planes
Animal Kingdom:
A Bugs Life - watch
Lion King (attraction reenacts movie)
Finding Nemo (attraction reenacts movie)
Land Before Time (not Disney but worth it for all the dino tie ins, especially at the ages listed)
Up - watch if plan on doing wilderness badges, makes more sense
Movies/ characters with some type of reference that tend to repeat throughout more than one park are:
Finding Nemo
Lion King
Pirates of the Caribbean
Aladdin
Beauty and the Beast
Little Mermaid
Toy Story
Snow White
Winnie the Pooh
And of course Mickey and his friends are everywhere.
* no promises I didn't forget something.