Oil is the Key
Most adhesives are oil-soluble. This means oil will break them down.
Cooking Oil
Apply a little vegetable oil, olive oil, or even peanut butter to the sticky spot. Let it sit for a few minutes, then rub it off with a cloth. Wash the area with soapy water to remove the oil.
Rubbing Alcohol
For glass or plastic, rubbing alcohol works well. Soak a cotton ball and rub the residue until it lifts.
Heat
For old stickers, use a hairdryer to warm the adhesive. This makes it easier to peel off. Follow up with oil or alcohol to remove any remaining glue.