An extruder or other similar tool head of a three-dimensional printer is slidably mounted along a feedpath of build material so that the extruder can move into and out of contact with a build surface according to whether build material is being extruded. The extruder may be spring-biased against the forward feedpath so that the extruder remains above the build surface in the absence of applied forces, and then moves downward into a position for extrusion when build material is fed into the extruder. In another aspect, modular tool heads are disclosed that can be automatically coupled to and removed from the three-dimensional printer by a suitable robotics system. A tool crib may be provided to store multiple tool heads while not in use.