I watched this with my kids last Christmas as a school project, and they both loved it. You can't beat the mean demeanor that Alastair Sim creates, nor the incredible, joyous change that he acts through. Wonderful messages about being generous and kind throughout the entire year (not just at Christmas), how having loving family and friends can bolster you, and what Victorian England was like without it being too scary or violent for younger viewers.
A great antidote to the cynicism surrounding Christmas.
This is a wonderful movie, a classic. The story of Scrooge's redemption and return to life "among the living" as someone who keeps the messages of kindness, gratitude, and charity towards his fellows is one that has been obscured by countless re-tellings and absorption into pop culture. There are two deathbed scenes, and the climactic scene where Scrooge faces the reality of his own death, and they are sad (for different reasons), but I wouldn't prevent my son from watching them. The Ghost of Christmas Yet to Come is presented as a black-robed faceless figure, Death-like, and this can be frightening for younger children. Also, there is a scene where the Cratchits, including the children, have a round of gin punch, but there is no drunkenness or inappropriate behavior--this is just a matter of historic and textual accuracy.