How to block dragging if collider hits

If the objects you want to drag can be rigidbodies, move them by setting the velocity, not the position - it allows the object to respect collisions.
The script below picks a rigidbody when the left mouse button is pressed, and drags it while the button is pressed. Instead of setting the object position, the script calculates the difference between mouse and object positions, and apply a proportional velocity to the object. Velocity is limited to maxSpeed to avoid the object to pass through thin objects. speed is a speed factor which controls how fast the rigidbody will follow the mouse pointer.

var speed: float = 5; // speed factor var maxSpeed: float = 15; // speed limit private var dragObj: Transform = null; private var hit: RaycastHit; private var length: float;

function Update(){

 if (Input.GetMouseButton(0)){  // if left mouse button pressed...
     // cast a ray from the mouse pointer
     var ray = Camera.main.ScreenPointToRay(Input.mousePosition);
     if (!dragObj ){  // if nothing picked yet...
         // and the ray hit some rigidbody...
         if (Physics.Raycast(ray, hit) && hit.rigidbody){
             dragObj = hit.transform;  // save picked object's transform
             length = hit.distance;  // get "distance from the mouse pointer"
         }
     } 
     else {  // if some object was picked...
         // calc velocity necessary to follow the mouse pointer
         var vel = (ray.GetPoint(length) - dragObj.position) * speed; 
         // limit max velocity to avoid pass through objects
         if (vel.magnitude > maxSpeed) vel *= maxSpeed / vel.magnitude;
         // set object velocity
         dragObj.rigidbody.velocity = vel;
     }    
 }
 else {  // no mouse button pressed
     dragObj = null;  // dragObj free to drag another object
 }

}

EDITED: This is a CharacterController version. It uses no gravity, and the objects stay at the position you release them.

var speed: float = 10; // speed private var dragObj: Transform = null; private var hit: RaycastHit; private var length: float; private var character: CharacterController;

function Update(){

 if (Input.GetMouseButton(0)){  // if left mouse button pressed...
     // cast a ray from the mouse pointer
     var ray = Camera.main.ScreenPointToRay(Input.mousePosition);
     if (!dragObj ){  // if nothing picked yet...
         // and the ray hit some character...
         if (Physics.Raycast(ray, hit)){
             character = hit.transform.GetComponent(CharacterController);
             if (character){
                 dragObj = hit.transform;  // save picked object's transform
                 length = hit.distance;  // get "distance from the mouse pointer"
             }
         }
     } 
     else {  // if some object was picked...
         // calc mouse pointer displacement
         var mov = ray.GetPoint(length) - dragObj.position; 
         // set object velocity
         character.Move(mov * speed * Time.deltaTime);
     }    
 }
 else {  // no mouse button pressed
     dragObj = null;  // dragObj free to drag another object
 }

}