Dungeon level

The dungeon level is displayed to the far left of the status line. You start the game on dungeon level 1, where it might read:

Dlvl:1  $:1699 HP:13(13) Pw:5(5) AC:8  Xp:1/0 T:1

The type and difficulty of monsters generated are based on the dungeon level.

Special dungeon levels

Dungeon level 0 is "nowhere". Attempting to teleport there via controlled level teleport is fatal, but you will get a warning:

Go to Nowhere.  Are you sure? [ynq] (q)

If you decide to answer yes, you die:

You scream in agony as your body begins to warp...
You cease to exist.  Your possessions land on the floor with a thud.

Your type of death will be recorded as suicide.

Dungeon levels -1 to -5 are the elemental planes and the astral plane. These are not accessible via teleportation, so the numbers are only useful in wizard mode. If you attempt to teleport to any level between -1 and -9, you find yourself high above the clouds, and plummet to your death:

You are now high above the clouds...
Unfortunately, you don't know how to fly.
You plummet a few thousand feet to your death.

If you are polymorphed into a monster which can fly, you float to the ground, and escape the dungeon:

You are now high above the clouds...  You fly down to the ground.

Teleporting to level -9 additionally gives the message:

You feel deliriously happy.   (In fact, you're on Cloud 9!)

Teleporting to level -10 or higher sends you to heaven:

You arrive in heaven.  "Thou art early, but we'll admit thee."

Your death is then recorded as "went to heaven prematurely".