Goo Gone-that stuff is amazing. We'd use it at work. Although I never seem to have any home when I need it! I remove labels from plastic jars occasionally. I'll use empty peanut butter jars to hold the random bits of rusty metal I pick up on my walks. And there's this one brand of couscous that comes in nice clear square jars with a screw on lid. They're nice to have to store bulk grains and such from the health food store.
I've tried baby oil, vegetable oil, and vaseline to remove the gummy residue, and been less than overwhelmed by the results. This may sound odd, but a squirt of spray furniture polish like Pledge also helps sometimes. Nail polish remover on a cotton ball can help. Soaking said jar in a sink of hot soapy water helps most of all. The paper will just rub right off, and it seems to make the residue a bit easier to remove. One thing I have heard but not tried yet is using a hair dryer on the sticky residue, to soften it up.
And glass or plastic jars,manufacturers use different adhesives, or some use boatloads while others skimp. I'd try whatever you happen to have on hand and see if that does it for you, before you make a trip to the store to buy goo-gone. One of the ideas above just may work for what you need.