I carry a few different forms of Tenacious Tape with me. Have used it several times for repairing bag edges (even checked luggage), backpack pockets, etc.

I think zipper breaking is a different story. It has happened to me a few times but I have had two zippers - one from each end -- and the other one is still working and will close the zip. If I could not close the zip I would try and find a luggage strap or similar wrap-around/bungee with tension. For example the zipper on my checked bag popped at some point during my Tokyo flight this past weekend -- came around the carousel and the whole main compartment was open -- but nothing had fallen out because I have a luggage strap around it. I would think something similar where you tape most of the gap but if you still need an opening, put the strap around and over that part to keep it closed but still accessible.

Then again, I travel with several fold-out bags so even after securing, probably putting the whole bag in one of those like Global Adventurer linked above.