Having recently rewatched "The King and I", which I saw as a youngster, I greatly enjoyed the film. Adults will enjoy the chemistry between Deborah Kerr and Yul Brynner (which his then-wife Doris characterized as "trusting each other like brother and sister off screen"). Kids will love the upbeat songs about whistling to overcome fear of a new situation, and getting to know a new culture. The secondary plot of an unhappy slave girl will, I think bore the kids and go right over their heads, which is ok. This plot has the only concern I have, that the King brandishes a whip and threatens to whip her. This is scary, but is made into a positive role message when Anna tells him that if he does, "He is truly a barbarian!" At which point the King throws down the whip and storms from the room.
The role of the King is much richer than I remember. His song "Puzzlement" is a poignant reminder about how we all have to do our best day by day as adults, just as the king does. The play deals with human rights, as shown in the "Small Cabin of Uncle Tom" scene, which is magical; and feminism in the feisty nature of Anna and her assertiveness in the face of the sexist King. None of this gets into the way of the film being great family fun, and I agree with the reviewer above that it is a great movie to spur family discussion about getting to know more about others -- and to do your best day by day.