Old Yeller. The theme song is iconic,

and even though it was made in 1957, the movie is still famous today for the emotional impact that it has on its audience.

I can't think any of their other movies that had such a powerful emotional impact. The only family movies I can think of that come close are Bridge to Terabithia, My Dog Skip, and Remember the Titans. The first two weren't Disney. I just learned that Remember the Titans was by Disney, but I don't think it had quite the same reach as Old Yeller. Disney was killing off beloved characters while George R. R. Martin was still in grade school.

And of course, everyone loves cute dogs. ; -)