I'd always shown my kids "adult" films because I thought they'd like them-- Monty Python and the Holy Grail was probably the biggest hit. My youngest daughter would often wake up and just sit down with me to watch whatever I was watching. My biggest surprise was when she sat down to watch most of Passion of Joan of Arc with me. The movie was surprisingly captivating to both of us.
When I was still homeschooling my kids in grade school, I decided that their summer break would be watching classic movies that they'd never seen, but needed to. I had them watch:
King Kong
Singin' In the Rain
Duck Soup
It's a Wonderful Life
Thief of Baghdad (1940) (would this count as a kids movie?)
As well as others. None of these were really successful, but they were remembered. Well, mostly.