I assume you want to understand everything you see going on in the parks. I'm going to list a lot, but just watch what you're willing and able to watch.
In general, you should see the popular animated movies. Just a warning: this includes A LOT of princess movies. Other movies you should see I'll list by park.
For MK: Monsters Inc. and Lilo & Stitch for Tomorrowlan; Fantasyland is where these princess movies come into play as well as Alice in Wonderland, Dumbo, Peter Pan, and either Winnie the Pooh movie; for Adventureland, the only movie that would help to watch would be Aladdin (and only marginally); Frontierland and Liberty Square don't really have any movies that could be applicable. The movies referenced in the Main Street Electrical Parade are the Tinkerbell series, Dumbo, Alice in Wonderland, Cinderella, Peter Pan, Snow White, Pinocchio, and Pete's Dragon.
In Epcot, all that would apply would be Finding Nemo, The Lion King, The Three Caballeros and/or Saludos Amigos, and soon, Frozen.
Hollywood Studios has way too many to list. Star Wars and Indiana Jones would be a big help (unless Indy's show closes).
For Animal Kingdom, you could watch A Bug's Life, The Lion King (again), and DINOSAUR (from 2000).
I've listed way too much and I doubt you'll watch all of them, so just pick and choose if anything I listed appeals to you. I hope this helps!