Old Yeller is in a league of its own, as far as I am concerned. Modern culture still references it. (See the modern country song that says he didn't cry when he saw it.) It, along with Pollyanna, Mary Poppins, and perhaps Swiss Family Robinson and The gy Dog and The Absent-Minded Professor and Treasure Island and The Parent Trap and Summer Magic should all be in rotation to be shown on TV regularly, as they once were.
I think Old Yeller and Mary Poppins both would still do well to be re-released in the theatres with the right promotion and timing. Generations love these films.
I think that Old Yeller has universal themes with which nearly every boy, and even most girls, will identify. As I watched it as an adult I was struck with the responsibility placed on Travis, as his father left for a long time to go into town. And it was not out of place for its time (the west of the 1860s). It helped him grow into a man. And his father believed in him, having given him the tools to do it in the first place. And his mother did not coddle him. She loved him and took care of him when he was injured, but still let him grow and take responsibility to be "the man of the house" while his dad was gone. He grappled with sibling rivalry, puppy love (literally and figuratively), disaster, irritation, and disease -- and also had some fun and adventure along the way.
What a story for modern audiences. And so gorgeously filmed.
Every generation needs to see this film, I think.