A monster, probably in the y or e class, with an attack that steals an item (or a few items, excluding equipped gear) from your inventory and randomly teleports it somewhere on the same level. This makes object detection and detect treasure nice to use even after a level is fully explored.

Change the Master Key of Thievery’s invoke power, since it already gives you guaranteed untrapping passively. The new invoke power is to magic map a moderate radius around you (maybe 10) and then teleport you (which will be controlled because the Key gives you teleport control), but you must pick a space within the mapped radius to teleport to.

If you controlled teleport to the same spot as an engulfing monster, there is a chance of teleporting inside it and being instantly engulfed instead of landing somewhere else.

Teleporting no longer checks to see if there is a monster present on the destination tile. Teleporting into a monster’s space has a chance of telefragging and instakilling it. (Though for fairness this should also happen to the player if a monster randomly teleports onto their space.)

Allow the player to teleport directly onto a magic portal.

A spell or other magic item or ability that can be used to apply an effect to a monster that prevents them from teleporting, levelporting, or warping.

Archons block teleportation on any level they’re on like demon lords do, because they’re otherwise too easy to avoid.

If the player attacks a monster in melee immediately following a teleport (possibly only a spontaneous teleport), they get a backstab bonus on it, even if they’re not a Rogue.

Teleport vortex, a monster which moves around the level sucking up items into its inventory; items in its inventory are periodically teleported randomly around the level. If it engulfs the hero, it will do the same.

If teleportation fails because there is a trap or monster on the destination square, and there is an adjacent free square, you get placed on that square, possibly with a message explaining why you didn’t end up exactly where you wanted.

When you attempt to teleport to a square containing a monster, you exchange places with it rather than having the teleport fail and send you somewhere random. This possibly fails based on a monster magic resistance check.

Spell that lets you do a random uncontrolled short-range teleportation, in order to escape from a tricky situation. Actually, it might not be a bad idea to turn the spell of teleport away into this, with a reduced level (3 or 4), and make it unable to shoot a teleportation beam.

If you release a djinni whose response is to say “It is about time” and vanish, the djinni will at least teleport you somewhere safe if you are in danger (not specified what defines danger; perhaps stuck in lava/rock or if there are a number of nearby hostile monsters).

Teleport at will shouldn’t be gained at different experience levels for Wizards versus everyone else - it should be standardized at the same level for all characters.

If you fall into water with teleport-at-will, the game should use casting a teleport spell as its last resort, once you have no other options for escape. It’s very annoying to attempt to teleport and lose energy and nutrition when you’re deliberately trying to jump in the water and can easily climb right back out.

When a monster teleports away, show a message “The foo disappears!” Possibly, if you also see where they teleported to, show another message, or just print “The foo teleports!” instead of printing a disappearance message.

In wizard mode, attempting to teleport into inaccessible terrain or into or out of a teleport region should prompt the player to confirm the teleport. If they confirm, they override any restrictions; if not, it prints “Sorry…” and works like normal.

Breaking a wand of teleportation will teleport as many monsters around you as there are charges left in the wand, always including yourself.

The scroll of teleportation now levelports when blessed and limits your possible teleport destinations to a small radius when cursed. Confused teleport gives you a single controlled horizontal teleport.

The Amulet of Yendor blocks teleporting within a dungeon level, but only after a certain radius. Short-range teleports work fine.

Armed bear traps and land mines can be teleported away if hit with a teleportation beam.

When a pet eats a teleportitis-granting corpse, it randomly teleports (if possible).

Allow teleportation onto the vibrating square, since it isn’t really a trap.

Monster flag M3_TELWITHU. Monsters with this flag (examples: quantum mechanics, some devils) will follow you when you teleport horizontally.