How to make a gameobject be exactly where the mouse is.

Simplest way is to do this:

 transform.position = Camera.main.ScreenToWorldPoint(Input.mousePosition)

But you're not going to get a depth position that's useful because your mouse has no inherent 3D location, it has a 2D location in the viewport, so the depth will probably be returned as the depth of the camera.

To get usable depth I've used two different methods.

1 - Set the depth manually.

 var x = Input.mousePosition.x;
 var y = Input.mousePosition.y;
 transform.position = Camera.main.ScreenToWorldPoint(Vector3 (x, y, yourZdepth));

The downside here is that the object won't always look like it's where the mouse is on the screen.

2 - Use ScreenPointToRay with a virtual plane.

 var plane : Plane = new Plane(Vector3(0, 1, 0),  Vector3(1, 1, 0), Vector3(1, 0, 0));

Then in Update():

 var ray : Ray = Camera.main.ScreenPointToRay(Input.mousePosition);
 var rayDistance : float;
 if(plane.Raycast(ray, rayDistance)) {
     targetPosition = ray.GetPoint(rayDistance);
 }
 transform.position = targetPosition;

Make the movement smoother by doing something like:

 transform.position = Vector3.SmoothDamp(transform.position, targetPosition, velocity, 0.05);

EDIT - You could also use ScreenPointToRay but then do a raycast against the scene geometry instead of that virtual plane to get a point on your game world surfaces.

All code is untested but should get the general point across.

I think what you want is this.

Camera.main.ScreenPointToRay(Input.mousePosition).GetPoint(_distanceFromCamera);