Who doesn't love a before and after picture. Unfortunately, I don't have one, and hope a reader will forward the photos after they've tried this trick.
Peanut butter!* Yep, just slather some on the gum, work it in and the gum will slide off after a few minutes.
Tested just yesterday on an eight year old. (The peanut butter was "organic" of course.)
*If you or your loved one has a peanut allergy please do not use peanut butter.