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A wand of digging is very effective. You can zap it to dig open a corridor of several squares (unless you're in a maze level, in which case the beam will continue as normal but will end after digging one wall square). Closed doors are broken through; as-of-yet-undetected secret doors are cleared.
Monsters that have one like to zap it downward and escape, which identifies it for you. If you zap it upward, a rock will fall from the ceiling and bonk you on the head, unless you are underwater, in which case you get the message "You barely hear some noises".
Engraving with a wand of digging automatically identifies the wand. Any text engraved with a wand of digging is as durable as text engraved with a weapon or hard gem. Wands of digging can engrave Elbereth in one turn, making them as effective as an athame for that purpose and slightly less effective than a wand of fire or wand of lightning.
If the current dungeon level has an undiggable floor, zapping the wand downward will make a pit. If this happens on a level with an ordinary maze, it's time to look for the vibrating square. Monsters that try to dig downward through an undiggable floor will simply fail to dig.
Except on undiggable floors, you cannot make a pit by zapping a wand of digging; it always makes a hole. The exception to this rule is if you dig down while standing on a trap - the trap will be destroyed and replaced by a pit (quite useful if you want to avoid accidently polymorphing a high level pet on a polymorph trap for example).
Note, however, that a wand of digging will not destroy boulders.
If you break a wand of digging with non-zero charges, 9 pits are created in a 3x3 square around you.
Wands comprise 4% of all randomly-generated items in the main dungeon, 6% in containers, 5% on the Rogue level, and 8% in Gehennom. There is a 5.5% chance that a randomly-generated wand will be a wand of digging.