I must be made of stone, because Goodbye Mog leaves me cold. I love Judith Kerr, and I was far more sad than I should have been when she died, and she is honestly one of the people I would most like to be like. But, while I think Goodbye Mog is beautifully written, to me it isn't horribly sad.
OTOH, @AgentCooper, I was also quite worried when I first read 10 Little Dinosaurs, that it would have an ending I couldn't cope with!
Bridge to Terebithia caught me and DP off-guard - she remembered it as a lovely heart-warming child's film, so we merrily watched it one day and both had to stop in floods of tears as DD watched in bemusement. She must have blanked out the tragic bit!
I also cry at The Selfish Giant, and the more because of that bit in the film Wilde where he tells the story to his own sons. Who, of course, he didn't get to see again after he got out of prison. 
And I had proper floods of tears when I decided - the first day DD went to nursery, of course, like an idiot - to re-read Anne's House of Dreams where her first baby dies, and she's not allowed to hold it or have it with her after the first few hours, because it's slowly dying and the wisdom of the time was that she shouldn't be told.
Awful to think of that.