•Tarzan, not surprisingly, given that Tarzan lives in the jungle and is a case of "Does Not Wear Clothes". Shortly after meeting him, Jane ditches her shoes and becomes a barefooter as well.
Esmeralda in The Hunchback of Notre Dame wore shoes in Hugo's novel (though her outfit was "tinsel and rags,") but goes barefoot in the Disney Animated Canon version. In the sequel, she gains a pair of shoes - presumably as she's now married to Phoebus, and can now afford a pair.
Kida in Atlantis The Lost Empire. Like Esmeralda, she ended up wearing shoes in the sequel. Also, Word of God actually confirmed that Kida was actually wearing Greco-Roman-style sandals at the end of the first film (they are hidden underneath her dress, and are the same shade of tan as her skin, but darker).
The title character in Pocahontas. And yes, she too ended up wearing shoes in the sequel (and at the theme parks, along with the two mentioned above). Seem to be seeing a pattern here with Disney Sequel Barefooters?
Aurora in Sleeping Beauty, at least as humble peasant girl "Briar Rose." When she gets her princess outfit and goes to the palace, then she's got shoes.
Giselle in Enchanted, though only in the animated segments. Possibly a direct reference to Aurora.
Once she gets feet, Ariel in The Little Mermaid goes barefoot more often than she wears shoes. Her daughter Melody in the sequel is a dedicated barefooter, only wearing shoes when she's forced to.
Rapunzel in Tangled. Of the youthful innocence variety — plus she's just never needed shoes due to never leaving her tower. Coincidentally, Rapunzel's voice actress, Mandy Moore, goes barefoot a lot in Real Life.
Lilo and Nani from Lilo & Stitch normally don't wear shoes at home, likely due to the Hawaiian tradition of going barefoot.
Mama Odie from The Princess and the Frog. Justified, since she is blind and possibly needs them bare.
Ralph from Wreck-It Ralph doesn't wear shoes, even when attending Felix's wedding as his best man. Part of it is probably to enforce his "Wild Man" character design, but it might also be because his feet are enormous.
•Jack Frost from Rise of the Guardians. At one point, elves try to give him a pair. With bells. They are quickly dismissed and never spoken of again.
The entire cast of The Croods — at least until Guy introduces them to shoes.
The Avengers and Iron Man 3: After Pepper Potts starts a relationship with Tony, she's often seen being barefoot once they start living together. Along with her more casual clothes, it's a sign of how they're able to relax around each other. (The practical reason for this is that Gwenyth Paltrow is several inches taller than Robert Downey Jr. and the filmmakers will take what they can get to keep them in frame together)
Fawn from Disney Fairies goes barefoot in her summer outfit as seen in "Great Fairy Rescue", the beginning of "Pixie Hollow Games", and several of the Pixie Previews. Vidia always wears shoes in the movies, but in the books she is a barefooter. A few fairies who have so far only been seen in the books are barefooters as well.