How to Make the FPS Character Controller RUN and CROUCH

The basic idea is simple: use different speeds when walking, running or crouching, and to crouch reduce the character vertical scale (remember to fix the character position while standing up to avoid falling through the floor). But if you are using the First Person Controller that comes with Unity, however, this may be a really hard job: it uses CharacterMotor.js, a very complicated script that usually drives crazy anyone who try to modify it. I know this very well: I was one of them... but I survived, and learned enough to do some tricks - including this!
To avoid editing the terrible CharacterMotor.js, I put all the code in this script; attach it to the First Person Controller, and they will communicate and do the magic:

 var walkSpeed: float = 7; // regular speed
 var crchSpeed: float = 3; // crouching speed
 var runSpeed: float = 20; // run speed
 
 private var chMotor: CharacterMotor;
 private var tr: Transform;
 private var dist: float; // distance to ground
 
 function Start(){
     chMotor = GetComponent(CharacterMotor);
     tr = transform;
     var ch:CharacterController = GetComponent(CharacterController);
     dist = ch.height/2; // calculate distance to ground
 }
 
 function Update(){
 
     var vScale = 1.0;
     var speed = walkSpeed;
     
     if (chMotor.grounded && Input.GetKey("left shift") || Input.GetKey("right shift")){
         speed = runSpeed;
     }
     if (Input.GetKey("c")){ // press C to crouch
         vScale = 0.5;
         speed = crchSpeed; // slow down when crouching
     }
     chMotor.movement.maxForwardSpeed = speed; // set max speed
     var ultScale = tr.localScale.y; // crouch/stand up smoothly 
     tr.localScale.y = Mathf.Lerp(tr.localScale.y, vScale, 5*Time.deltaTime);
     tr.position.y += dist * (tr.localScale.y-ultScale); // fix vertical position
 }

EDITED: @bacca87 posted a C# version below, and also included a fix to avoid run speed while in the air - feature that I've added to this answer.

EDITED 2: The script above works, but has the bad collateral effect of modifying the vertical scale of any character child - like the weapon, as @Fishman92 noticed! To avoid this, the version below modify the character height instead of its vertical scale:

 var walkSpeed: float = 7; // regular speed
 var crchSpeed: float = 3; // crouching speed
 var runSpeed: float = 20; // run speed
 
 private var chMotor: CharacterMotor;
 private var ch: CharacterController;
 private var tr: Transform;
 private var height: float; // initial height
 
 function Start(){
     chMotor = GetComponent(CharacterMotor);
     tr = transform;
     ch = GetComponent(CharacterController);
     height = ch.height;
 }
 
 function Update(){
 
     var h = height;
     var speed = walkSpeed;
     
     if (ch.isGrounded && Input.GetKey("left shift") || Input.GetKey("right shift")){
         speed = runSpeed;
     }
     if (Input.GetKey("c")){ // press C to crouch
         h = 0.5 * height;
         speed = crchSpeed; // slow down when crouching
     }
     chMotor.movement.maxForwardSpeed = speed; // set max speed
     var lastHeight = ch.height; // crouch/stand up smoothly 
     ch.height = Mathf.Lerp(ch.height, h, 5*Time.deltaTime);
     tr.position.y += (ch.height-lastHeight)/2; // fix vertical position
 }

NOTE: The white capsule childed to the FPC ("Graphics") isn't modified by this script, thus it will sink a little in the terrain when crouching. A similar problem will happen when the player crouches under a low ceiling: the top of the capsule will penetrate the ceiling. This makes no difference, since "Graphics" doesn't have a collider.