First is a video showing some cutting tricks for a Möbius strip. I show this to my topology class, then have them play around with Möbius strips—twisting them various numbers of times and cutting down the middle or in thirds. One of my favorite examples is to pass the paper strip through a wedding ring, give it three half-twists and tape together. Cut the loop of paper down the center and the paper will form a knot around the ring. (I wrote about this trick here. It is attributed to Stanley Collins.)
Finally, for fun, how to do origami with the NetFlix envelopes.