Multiple-block downhole anchors and anchor assemblies are provided. A downhole anchor assembly for a tubing string includes an anchor block, a drag block, a biasing arrangement, and a mandrel to be coupled to the tubing string. The anchor block moves, with rotation of the mandrel, between a run position out of contact with a well bore and a set position in contact with the well bore to set the downhole anchor assembly in the well bore. The drag block contacts the well bore at least when the anchor block is out of contact with the well bore. The biasing arrangement biases the anchor block away from the well bore and the drag block toward the well bore. The anchor block is thus protected from the well bore by the drag block, and the biasing arrangement provides for automatic un-setting of the anchor block when torque is removed from the mandrel.