Blocked tear ducts. The most common causes of sticky eyes in newborns are either blocked tear ducts (that drain tears from the eyes to the nose) or conjunctivitis (an infection of the skin lining the inside of the eyelids and the outside of the white of the eye). Blocked tear drains eventually open on their own in most children by 1 year of age, but see an eye doctor to determine the best course of action.
How new? If they are brand new (one or two days old) then this could be just the antibiotic salve that is put into all new babies eyes. It may also be excess tears from tear duct blockade, especially if there is no redness or swelling. It could also be conjunctivitis ("pink eye") if the stickiness is from excessive "eye goobers.".