Super Glue
If you have a pair of shoes that need repairing this is what you need. I used it to stick back the sole on one of my sons shoes a couple of months ago and it hasn't come unstuck yet. Apparently you can use it to build up worn heels. If you don't use the whole tube it can be stored in the freezer once you have opened it.
The same firm makes Tenacious Tape which is really um… Tenacious.