Duct tape is good for a great many things, but if you're sick of the sticky, messy hassle, Rescue Tape is a pretty great alternative. It sticks only to itself, and can patch holes, act as shrink-wrapping, or even mend wounds.
Rescue Tape is kind of like a Fruit Roll Up, in the sense that it's stretchy, sticks only to itself, and can withstand a ton of heat, electricity and pressure. You can use it for just about anything, big or small - fixing pipe leaks, protecting boards while you're soldering, or even just as an impromptu bandage. And, best of all, it doesn't leave behind the awful residue that other tape does, despite its strength. The video above is pretty cheesy, but actually does a good job of explaining the hard-to-put-into-words product.
Rescue Tape is really just one brand of silicone tape; you can probably find something similar at your local hardware store. Just search for silicone tape and you should find a product that will work. Hit the link to read more.