In this work, the authors aimed to identify a potential correlation between the printability and crucial rheological characteristics of materials involved in fused deposition modeling (FDM) technology. In this regard, three different poly(lactide) acid (PLA)-based filaments (two commercially available (here called V-PLA and R-PLA) and one processed in a lab-scale extruder (here called L-PLA)) have been considered. Dynamic rheological testing, in terms of frequency sweep at five different temperatures (130, 150, 170, 190, and 210 °C), was performed. Rheological properties expressed in terms of viscoelastic moduli and complex viscosity curves vs. frequency, characteristic relaxation times, activation energy (Ea), zero shear viscosity (η0) and shear thinning index (n) were derived for each material. A characteristic relaxation time of around 0.243 s was found for V-PLA, a similar value (0.295 s) was calculated for R-PLA filaments, and a lower value of about an order of magnitude was calculated for L-PLA filament (~0.0303 s). The activation energy and shear thinning index resulted to be very comparable for all the filaments. On the contrary, V-PLA and R-PLA possessed a zero-shear viscosity (~104 Pa*s at 170 °C) much higher than L-PLA (~103 Pa*s). All the filaments were processed in a 3D printer, by attesting the effect of nozzle temperature (180, 190, and 210 °C, respectively) on printing process, and macroscopic shaping defects in printed objects. Final considerations allowed us to conclude that polymer relaxation time, zero-shear viscosity, and melt viscosity (affected by printing temperature) were critical parameters affecting the printing quality.