Study the damaged area of the DVD. A hairline crack might be repairable. A crack near the center hole of the disk that doesn't reach the data area may also be repairable.
Hold the cracked DVD up to a bright light and examine the disk. If you can see damage in the foil layer of the disk (the part that stores the data), the disk is permanently damaged. Even a pin hole can render a disk unreadable.
If the disk is completely cracked in pieces, it is not repairable. Contact the manufacturer for a replacement disk.
Fill the crack with plastic-safe super glue. Use a toothpick to apply the glue directly to the crack. Allow to dry.
Prevent further damage to the DVD by covering it with a fresh disk label. Make sure you apply the label to the non-readable side of the disk. A two-sided disk can not be covered with a label.
Replace the storage case with a plain CD style jewel box that does not have a center "claw" for the hole of the DVD. Popping the disk in and out of the claw can stress the DVD and increase the damage.