I'm not sure it's the best way, but you could just have a boolean that you toggle in OnMouseDrag and OnMouseUp, and then check that the GameObject isn't being dragged in OnTriggerEnter.

i.e.

var beingDragged : boolean = false;

void OnMouseDown()
{
    originalPosition = transform.position;
}

void OnMouseDrag()
{
    // Get our current mouse position
    currentPosition = Camera.main.ScreenToWorldPoint(Input.mousePosition);

    // If we don't set z to blocks orig z it will put the block at 0
    // with camera and put it out of view
    currentPosition.z = transform.position.z;

    // Move object each frame with mousedrag active
    transform.position = currentPosition;

    // Hide mouse cursor
    Screen.showCursor = false;

    beingDragged = true;
}

void OnMouseUp()
{
    beingDragged = false;

    // Show mouse cursor
    Screen.showCursor = true;

    // On mouse up move block to original position for now
    transform.position = originalPosition;
}

void OnTriggerEnter(Collider blockCollider)
{
    if (!beingDragged)
    {
        Debug.Log("We hit something!!!" + blockCollider.name + " " + blockCollider.tag);
    }
}

I had a quick search but couldn't find a simple method to find which object was currently 'selected' (i.e. the focus of a MouseDrag). I'd be interested in a better solution, but this should work.