Find a moving box that is large enough to hold your entire set of wineglasses, but do not use a box that is so large that it requires more cushioning than necessary.
Fold a plush bath towel. Line the bottom of the box with the folded towel.
Wrap each wineglass loosely in a sheet of newspaper. Tuck newspaper over the rims and under the stems of the wineglasses. Wrap an additional sheet of newspaper around each glass.
Lay the glasses down in a row in the box. Alternate glass positions so that the top of every other glass is next to the stem of every other glass.
Place another plush towel on top of the wrapped glasses. If necessary, add additional towels until they fit to the top of the box. The box should be packed firmly.
Seal the box. The My Great Home website recommends reinforcing moving boxes with packing tape.
Label the box with a bright red or black marker. In addition to "Fragile" warnings, write "Wineglasses" and their destination (e.g., dining room, kitchen) on the box.