The DevTeam Thinks Of Everything, initials TDTTOE, is a term used to describe the NetHack developers' writing messages for specific situations. This means that if you think of doing something "clever" in the game, the DevTeam most likely thought of that, and the game will then put out the specific response.
The phrase The DevTeam Thinks Of Everything highlights the fact that, of all the many actions possible for you to take in the game, the DevTeam has likely foreseen that particular action being taken and has programmed in a specific response for it. This is a contrast with many other similar roguelike games in which generic responses to actions will be displayed if nothing of any particular interest happens; though it must be noted that NetHack does have its fair share of those as well.
Examples of Messages
One example is that of throwing a cream pie at a monster:
The cream pie splashes over the jackal's face!
Another prominent example is seen when attempting to #dip a potion into itself:
This is a potion bottle, not a Klein Bottle!
Or, similarly, placing a bag inside itself:
That would be an interesting topological exercise.
You were wearing a blindfold. You still cannot see.
Thou hast angered me.
This is followed by a (usually) fatal bolt of lightning striking you from the heavens. However, with shock resistance, the attack can be survived. This is then repeated with a wide-angle disintegration beam, but with disintegration resistance, this can also be survived. If this occurs, then:
You bask in its black glow for a minute... [Your god] says: "I believe it not!"
Obviously, this example has much more effect on the actual gameplay than the previous trivial messages.