If graphene is ever going to live up to the promises of future nanoelectronic devices, an easy and cheap route for mass production is an essential requirement. A way to extend the capabilities of plasma-enhanced chemical vapour deposition to the synthesis of freestanding few-layer graphene is presented. Micrometre-wide flakes consisting of four to six atomic layers of stacked graphene sheets have been synthesized by controlled recombination of carbon radicals in a microwave plasma. A simple and highly reproducible technique is essential, since the resulting flakes can be synthesized without the need for a catalyst on the surface of any substrate that withstands elevated temperatures up to 700 degrees C. A thorough structural analysis of the flakes is performed with electron microscopy, x-ray diffraction, Raman spectroscopy and scanning tunnelling microscopy. The resulting graphene flakes are aligned vertically to the substrate surface and grow according to a three-step process, as revealed by the combined analysis of electron microscopy and x-ray photoelectron spectroscopy.