If you've never heard of 3M Transpore Tape, you really need to change that because this stuff is so handy to have around. In my opinion it's often better than typical band-aids when you need to bandage up a wound or cover a blister/cut/etc.

The tape is latex-free/hypoallergenic, tears off the roll easily, is porous enough to let skin breathe, is water-repellant (though not necessarily watertight), and holds in place very well even on damp skin, yet comes off relatively painlessly when you need it to.

Use the stuff by itself, cover plain band-aids with it to creature a more moisture-resistant layer, dress wounds in the field — or, you can get creative with the stuff while MacGyvering things around the house, doing electronics/soldering work, you name it.

There are a bunch of listings on Amazon for various sizes and amounts of Transpore tape, but to keep things simple, I recommend starting with this pack of twelve for $12 and keeping a roll or two in your first aid/survival kit.