The episode "Your Friend, Little Bear", when Emily has to go back to town to go to school. It's heartwarming as Little Bear learns to write so he can send her letters, but also a pretty sad moment for Little Bear, who won't get see his best friend again until the next summer. After she leaves, he's shown crying silently as Mother Bear rocks him in the rocking chair, and the next scene opens with him staring sadly out the window at the rain, still thinking of Emily. This is fortunately resolved in the second season, when she moves to the forest.
All the Sick Episode/s (A Flu, Little Bear's Sweet Tooth, Pillow Hill, Between Friends)
"Little Bear's Sweet Tooth" didn't even start out as a Sick Episode. It started off as a perfectly normal episode but when they end up with the pie Eating Contest, Little Bear starts groaning and not wanting to eat pies. That night at bedtime, his stomach still hurts and he claims he's lost his sweet tooth.
In "Between Friends", when Little Bear and Emily have the mumps, they look pitiful lying in bed and Little Bear can't even laugh without feeling pain. Also, Little Bear clearly feels guilty about giving Emily the mumps.
While "A Flu" wasn't that sad, since it had comedy, it was still kind of sad seeing Little Bear needing to stay in bed all day.
The main reason "Pillow Hill" is sad is because Little Bear's cold prevents him from having a picnic.
In "Lucy's Okay", Little Bear, Duck, Owl, and Emily pretend that Lucy died and they're having a funeral. But the funeral is so convincing that Owl and Little Bear actually feel sad and nearly forget that they're just pretending, and Duck completely forgets and she seems to be the most emotional, even crying instead of saying her fake eulogy. To make matters worse, they told Mother Bear, Cat and Hen that Lucy was dead without giving them the heads-up that it's just a serious "game". Emily admits to Cat and Hen that they were pretending, but Mother Bear is still uninformed (although she's likely rational enough to know dolls can't really die). Luckily, the episode has a Happy Ending where they realize that, just as the title says, Lucy's OK.
In "Emily's Balloon", using the titular balloon and his own, Little Bear is flying down to what he assumes is Emily's house and calls out to her only for the wind to pull him back, and he tells her goodbye.
"Emily's Birthday" has Little Bear upset that Emily is growing up, which he doesn't want her to do because it means she'll go away and he'll never see her again. He was already upset in "Your Friend, Little Bear" that Emily had to leave for school and wondered when he'd see her again, and here, he's afraid of reliving that.
Cub's separation from his parents, where they were trying to get through a terrible storm that caused a wildfire. Cub's parents pushed him out of the way to safety but got lost from him in the attempt. Doubles as Nightmare Fuel for any family. He hasn't seen them in ages and has basically been living alone.
