Composite products are often created using traditional manufacturing methods such as compression or injection molding. Recently, additive manufacturing (three-dimensional (3D) printing) techniques have been used for fabricating composites. 3D printing is the process of producing three-dimensional parts through the successful combination of various layers of material. This layering effect in combination with exposure to ambient (or reduced) temperature and pressure causes the finished products to have inconsistent microstructures. The inconsistent microstructures along with the oriented reinforcing fibers create anisotropic parts with difficulty to predict mechanical properties. In this paper, the mechanical properties of fiber-reinforced polymer composites produced by additive manufacturing technique (3D printing) and by traditional manufacturing technique (compression molding) were investigated. Three open-source 3D printers, i.e., FlashForge Dreamer, Tevo Tornado, and Prusa i3 Mk3, were used to fabricate bending samples from carbon-fiber-reinforced acrylonitrile butadiene styrene (ABS). Results showed that there exist significant discrepancies and anisotropies in mechanical properties of 3D-printed composites. First, the properties vary greatly among parts made from different printers. Second, the mechanical responses of 3D-printed parts strongly depend upon the orientations of the filaments. Parts with the infill oriented along the length of the specimens showed the most favorable mechanical responses such as Young’s modulus, maximum strength, and toughness. Third, all 3D-printed parts exhibit inferior properties to those made by conventional manufacturing. Finally, theoretical modeling has been attempted to predict the mechanical responses of 3D-printed products and can potentially be used to “design” the 3D printing processes to achieve the optimal performance.