This paper presents a set of simple and intuitive robot collision detection algorithms that show substantial scaling improvements for high geometric complexity and large numbers of collision queries by leveraging hardware-accelerated ray tracing on GPUs. It is the first leveraging hardware-accelerated ray-tracing for direct volume mesh-to-mesh discrete collision detection and applying it to continuous collision detection. We introduce two methods: Ray-Traced Discrete-Pose Collision Detection for exact robot mesh to obstacle mesh collision detection, and Ray-Traced Continuous Collision Detection for robot sphere representation to obstacle mesh swept collision detection, using piecewise-linear or quadratic B-splines. For robot link meshes totaling 24k triangles and obstacle meshes of over 190k triangles, our methods were up to 3 times faster in batched discrete-pose queries than a state-of-the-art GPU-based method using a sphere robot representation. For the same obstacle mesh scene, our sphere-robot continuous collision detection was up to 9 times faster depending on trajectory batch size. We also performed a detailed measurement of the volume coverage accuracy of various sphere/mesh pose/path representations to provide insight into the tradeoffs between speed and accuracy of different robot collision detection methods.