I make no secret of being a total sap. I also don't and (really can't) have kids, so sometimes just straightening up the kids' section makes me teary. The following, though, have threatened to reduce both me and Stephanie into quivering heaps of jelly:
This one's about coming back from terrible loss--I think the death of a parent.
This one's all friendship and frolic until three-quarters through, and then BAM! sucker punch.
This one's more poignant than "sad" per se--it's more or less an introduction to moral ambiguity for children. Petit just can't understand why he is sometimes good (like when he plays with his dog, and takes good care of his toys) and sometimes bad (like when he pulls hair and throws things at pigeons). "Am I some kind of not-yet-discovered type of monster?" he asks himself...mind-blowing stuff for a 5-year-old. Her (I think Isol is a her; ah, yes, says Wikipedia. Also Argentinian!) It's Useful to Have a Duck is also sniffle-inducing sweet.
Ditto with this one, where the eponymous bunny goes to visit his city-gal friend Little Rabbit and gets exhausted being rushed around to cafes and museums and parks. "I just wanted to show you everything!" she finally says; "But I came to the city to see you!" he responds. OMG SO SWEET AND SO TRUE I LOVE IT. Uh, and the illustrations are gorgeous too.
And on the other side of the spectrum, I've personally tested it several times, and I defy you to get all the way through Big Rabbit's Bad Mood without feeling better. It's great stuff!