Crouching in source ports consists technically in a modification of the player's height and lowering of the camera viewpoint. The reduced collision box can be used to pass through low passages or to dodge incoming projectiles. The latter can be seen as cheating since Doom monster AI was not designed to deal with crouching players, and so can the former if the map was not designed specifically for this feature. To compensate for the advantage of a smaller hitbox, player movements are usually slowed down when crouching.
The Doom 0.4 alpha featured a "prone" mode that could be seen as a prototype for crouching, ultimately removed from the game, or more likely as a way to test the camera lowering effect when the player dies.
Although not technically crouching, Heretic and Hexen allow, by their transformations in chicken or pig, to obtain the diminished hitbox permitting to pass through low passages. This is typically only possible in multiplayer, though it can be achieved in single player in Hexen by triggering the "reflective defense" of a centaur or slaughtaur then firing the porkelator at it to have a projectile bouncing back towards the player. In at least one map, it can be used to access a shortcut.
A more spectacular form of crouching is the death slide, which consists in deliberately getting killed while having enough momentum to pass through a low opening. The player's height when dead is reduced to 0, avoiding any vertical collision checks. However, this is only productive if allowing a suicide exit.