Cheap paper towels are the best wrapper for glass items when packing to move. It leaves no black ink residue the way newspaper does. It's thick and reliable and best of all, it can be used again after you unpack!
We used dish towels, dishcloths, tablecloths, even bath towels and sheets to wrap our glassware and plates when we moved. You've gotta pack it anyway, so you might as well put it to use!