In this study, the strain rate sensitivity of five different thermoplastic polymers processed via Fused Filament Fabrication (FFF) Additive Manufacturing (AM) is reported. Namely, Polylactic Acid (PLA), Acrylonitrile-Butadiene-Styrene (ABS), Polyethylene Terephthalate Glycol (PETG), Polyamide 6 (PA6), and Polypropylene (PP) were thoroughly investigated under static tensile loading conditions at different strain rates. Strain rates have been selected representing the most common applications of polymeric materials manufactured by Three-Dimensional (3D) Printing. Each polymer was exposed to five different strain rates in order to elucidate the dependency and sensitivity of the tensile properties, i.e., stiffness, strength, and toughness on the applied strain rate. Scanning Electron Microscopy (SEM) was employed to investigate the 3D printed samples’ fractured surfaces, as a means to derive important information regarding the fracture process, the type of fracture (brittle or ductile), as well as correlate the fractured surface characteristics with the mechanical response under certain strain rate conditions. An Expectation–Maximization (EM) analysis was carried out. Finally, a comparison is presented calculating the strain rate sensitivity index “m” and toughness of all materials at the different applied strain rates.