Custom collisions?

Hi there!

I have a very simple project set up, it's got 2 cubes in it, and one of the cubes has a movement script

void Update () {
    Vector3 moveDirection = new Vector3(Input.GetAxis("Horizontal"),
        0,
        Input.GetAxis("Vertical"));
    transform.position += moveDirection * speed * Time.deltaTime;
}

What I want is to know how to set it up so that if one box moves in to the other box, it can not move further in that direction. The catch is that I don't want either of the objects to be affected by physics, so rigidbodies are out of the question.

Rigidbodies are not out of the question, they are necessary if you want collisions. Set isKinematic to true and use rigidbody.MovePosition.