The artist Nicole Ondre makes striking ceramic sculptures based on knot theory.

Full disclosure, she is also my wife.

I have a theory about tying shoelaces. I tie mine in the "correct" way which doesn't reposition the loops vertically. Never thought about it until that viral TED talk. My son, however, does the opposite. Since I'm the one that taught him how to tie his shoes, my theory is that he watched me make knots, from the opposite side, and thus internalized making the same knot, but in reverse.

If my theory is true, then every other generation ties their knots in reverse...

The Theory of Yarn Structures is also interesting:
As an excellent application of knot theory, the video demonstrates two ways to avoid the problem of untangling messy earphone cords. The first one, which I happened to figure out by myself, is to store them confined to a tight space. The second one, which strains the cord a bit more but still appears practical, is demonstrated around 31:20.
Totally randomly, I visited cool link site Boing Boing to find “Orangutan Building a Hammock” with an overhand knot. Wow

Knot theory is not useless, topological quantum computation uses braids and knots extensively.
The title is misleading click batey but very interesting video about knot theory.

From the video it looks like mathematical knots might not have the property actually of being real knots that you can tie. Is this true? Does anyone know?

The course on knot theory was the most confusing part of my curriculum.