Years ago, one of my bags emerged on the baggage carousel popped open in terrible shape with the contents barely contained. My Le Creuset quiche pan had slipped out and was circling the carousel on its own (it survived. I don't usually travel with bakeware, I was moving back from living abroad). Unfortunately this very large, very damaged bag needed to be checked onto a further flight.

A kind airport employee -- TSA, I suppose, but maybe he was customs-- saw my predicament and offered me use of what in my mind I now think of as the "TSA Duct Tape," as it said "TSA" on it. It seemed official? And he assured me no one would mess with my bag on its final leg. So we taped up my bag, I checked it in, and I was on my merry way. All my belongings (including the Le Creuset dish, which I managed to stuff back in the bag) arrived at my final destination safely.

So, yes, you can absolutely use duct tape on your bags, and bonus points if you can get some that says "TSA" on it as well.