Automation of logistics tasks for small lot sizes and flexible production processes requires intuitive and easy-to-use systems that allow non-expert shop floor workers to naturally instruct transportation systems. To this end, we present a novel laser-based scheme for teach-and-repeat of mobile robot trajectories that relies on scan matching to localize the robot relative to a taught trajectory, which is represented by a sequence of raw odometry and 2D laser data. This approach has two advantages. First, it does not require to build a globally consistent metrical map of the environment, which reduces setup time. Second, the direct use of raw sensor data avoids additional errors that might be introduced by the fact that grid maps only provide an approximation of the environment. Real-world experiments carried out with a holonomic and a differential drive platform demonstrate that our approach repeats trajectories with an accuracy of a few millimeters. A comparison with a standard Monte Carlo localization approach on grid maps furthermore reveals that our method yields lower tracking errors for teach-and-repeat tasks.