This paper reports a novel, negligible-cost and open-source process for the rapid prototyping of complex microfluidic devices in polydimethylsiloxane (PDMS) using 3D-printed interconnecting microchannel scaffolds. These single-extrusion scaffolds are designed with interconnecting ends and used to quickly configure complex microfluidic systems before being embedded in PDMS to produce an imprint of the microfluidic configuration. The scaffolds are printed using common Material Extrusion (MEX) 3D printers and the limits, cost & reliability of the process are evaluated. The limits of standard MEX 3D-printing with off-the-shelf printer modifications is shown to achieve a minimum channel cross-section of 100×100 μm. The paper also lays out a protocol for the rapid fabrication of low-cost microfluidic channel moulds from the thermoplastic 3D-printed scaffolds, allowing the manufacture of customisable microfluidic systems without specialist equipment. The morphology of the resulting PDMS microchannels fabricated with the method are characterised and, when applied directly to glass, without plasma surface treatment, are shown to efficiently operate within the typical working pressures of commercial microfluidic devices. The technique is further validated through the demonstration of 2 common microfluidic devices; a fluid-mixer demonstrating the effective interconnecting scaffold design, and a microsphere droplet generator. The minimal cost of manufacture means that a 5000-piece physical library of mix-and-match channel scaffolds (100 μm scale) can be printed for ~$0.50 and made available to researchers and educators who lack access to appropriate technology. This simple yet innovative approach dramatically lowers the threshold for research and education into microfluidics and will make possible the rapid prototyping of point-of-care lab-on-a-chip diagnostic technology that is truly affordable the world over.