This paper presents a method for automatic segmentation, localization, and identification of vertebrae in arbitrary 3D CT images. Many previous works do not perform the three tasks simultaneously even though requiring a priori knowledge of which part of the anatomy is visible in the 3D CT images. Our method tackles all these tasks in a single multi-stage framework without any assumptions. In the first stage, we train a 3D Fully Convolutional Networks to find the bounding boxes of the cervical, thoracic, and lumbar vertebrae. In the second stage, we train an iterative 3D Fully Convolutional Networks to segment individual vertebrae in the bounding box. The input to the second networks have an auxiliary channel in addition to the 3D CT images. Given the segmented vertebra regions in the auxiliary channel, the networks output the next vertebra. The proposed method is evaluated in terms of segmentation, localization, and identification accuracy with two public datasets of 15 3D CT images from the MICCAI CSI 2014 workshop challenge and 302 3D CT images with various pathologies introduced in. Our method achieved a mean Dice score of 96%, a mean localization error of 8.3 mm, and a mean identification rate of 84%. In summary, our method achieved better performance than all existing works in all the three metrics.