Friction tape would be a good choice. It's not sticky, but it sticks to itself and positively vulcanizes to itself over time.

Standard electrical tape can be positively secured with a drop of superglue on the end. Another tip I learned recently is to not pull it apart. Cut it. That way the end isn't stretched. Stretching the end is the main thing that makes it unravel, as it shrinks back to its original length.

Finally, I always give it at least three extra loops on the end. That way if it does unravel, it doesn't work loose down the full length.