A MacGyver tip from Lifehacker says that you can use an old mousepad to open jars with stubborn lids. For a doctor like me, sometimes a mousepad is not that too handy. Even if I find one in the hospital or clinic, that isn't mine, and the officials concerned might not be too happy if I used their mousepads to open jars. *LOL*
Here's my own modification of that same tip --- for doctors, nurses, or paramedical personnel who might one day encounter stubborn jar lids. I use a rubber tubing, which is handy if you have those tourniquets used for venipunctures (blood extractions) around. Another daring attempt --- although you risk destroying it --- is the handy stethoscope's rubber tubing. Yes, I've tried this, and it works. And no, I didn't wreck my stethoscope.
Of course, if there's a burner or gas range nearby, it will make things much easier. You can try heating the stubborn lid on low fire for 5 seconds tops, before trying to open it with the rubber tubings. Heat expands the lid, making it loose and easy to turn.