Monsters have only a 1 in 3 chance of setting off a land mine when they step on one. Flying creatures are even less likely to set one off (and won't ever fall in the resulting pit), although there is still a slim chance that air currents will activate the mine. Land mines can also be set off by rolling boulders. Be careful, as you can set off your own land mines if you move on to that square or fail to untrap them.
Because monsters can often get past them, placing a single land mine is usually not that effective. However, you can set several mines to make a mine field, which might be handy for dealing with certain special rooms filled with monsters. You could also use a mine field to protect the area around a stash. The explosion will do 1-16 damage, and leave behind a pit. It can also be used as a warning system to alert you to the presence of monsters: "Kaablamm! You hear an explosion in the distance!"
Since some monsters tend to pick up items left lying around, you might be able to lure victims on to your land mines with bait that appeals to them. Any items on the same square as an active land mine will be blasted around the room (or destroyed, if fragile) when it goes off.
You can recover many land mines from the treasure room in Fort Ludios.