Children love this story because the adventure brings their imagination far far away from the classroom; yet the story smartly brings everyone back to reality in the end. It is so easy to set storylines to music. In class, I'd play leader and have all the children echo what I sing - as if we are really going on a bear hunt.
There are so many follow-up activities one can think of after reading the story.
As a music teacher, I choose role-playing and singing games as an extension, where we go through the story again with creative movement - this time, I'd play on the piano as the leader, children can choose to be any characters as they move around the room according to the storyline. - Yes, it'll be a bit chaotic, but it's SUPER FUN!
Art teachers may turn the story into a tactile lesson where children are guided to create the different scenes in the story (the grass, the river, the mud, the snow, the forest).
I can also imagine English teachers using this story to use the story to introduce onomatopoeia; and set a creative writing task according to the story structure.
Below is a video made inspired by the story. The words they use in the video is not 100% from the original story, but it gives you an idea of the many creative learning outcome this story may inspire.
We're Going on a Bear Hunt has been so well-received since it was first published. A live-on-stage version has been created. Here's the trailer of the show: