Ignore Weather allows the user to walk over swamps, marshes, and poison marshes regardless of weather, and is learned from the Oracle Job for 200 JP.
Levitate and Teleport are learned by Time Mages. Levitate causes the user to float above the ground, allowing them to move pretty much anywhere, while Teleport allows the unit to instantly reappear on any tile, though it has an increased chance of failing the farther they move. Master Teleportation is an ability some enemies have, which is the same as Teleport, but without the chance of failure.
Waterbreathing is a monster exclusive ability of the Mindflayer Family. It allows them to move and stop even when fully submerged in water of depth 3. Oddly enough, the ability has a cost of 200 JP.
Another exclusive monster ability is called Cannot enter water, this ability makes monsters unable to walk in water, restricting them to land terrain. This ability too has a cost of 200 JP.