We present an overview of recent X-ray observations of Wolf-Rayet (WR) stars with XMM-Newton and Chandra. A new XMM spectrum of the nearby WN8 + OB binary WR 147 shows hard absorbed X-ray emission, including the Fe K-alpha line complex, characteristic of colliding wind shock sources. In contrast, sensitive observations of four of the closest known single WC (carbon-rich) WR stars have yielded only non-detections. These results tentatively suggest that single WC stars are X-ray quiet. The presence of a companion may thus be an essential factor in elevating the X-ray emission of WC + OB stars to detectable levels.