The first time I encountered this, I didn't even know that what I had made was a non-Newtonian fluid. My mother was going through radiation therapy for her breast cancer (ductal carcinoma in-situ). She was instructed not to use any deodorant during that time. When she asked her doctor what she could do to minimize wetness and odor under her arms, he suggested that she try using a little cornstarch and water. He didn't give her any further instructions, so it was left to me to figure out how to make this work for my mom.
I found a little container and I tried to mix the two ingredients together. The result didn't look like anything that she could spread or dust under her arms. It was dry and weird feeling. What I didn't realize is that what I'd made is called oobleck. Here's a cool Youtube video showing how to make it.