This study presents a comparative analysis of the tensile properties of 3D-printed polymer specimens with different standard geometry shapes. The objective is to assess the influence of printing orientation and geometry on the mechanical performance. Rectangular-shaped ASTM D3039 specimens with angles of 0°, 15°, and 90° are compared to various tensile test specimens based on ASTM and ISO standards. All specimens are fabricated using polyethylene terephthalate glycol (PETG) material through fused deposition modeling (FDM). Two printing orientations, flat and on-edge, are investigated, and tensile strength, elastic modulus, strain, and elongation at break are measured. The study examines the weak spot commonly found at the neck of the specimens and evaluates the broken areas. Additionally, a numerical analysis using the finite element method (FEM) is performed to identify stress risers’ locations in each specimen type. Experimental results show that the ASTM D3039-0° specimen printed in the on-edge orientation exhibits the highest tensile properties, while the flat orientation yields the best results in terms of the broken area. The ISO 527-2 specimens consistently display lower tensile properties, irrespective of the printing orientation. The study highlights the enhanced tensile properties achieved with the rectangular shape. Specifically, the tensile strength of ASTM D3039-0° was 17.87% and 21% higher than that of the ISO 527 geometry shape for the flat and on-edge orientations, respectively. The numerical analysis indicated that the ISO 527-2 specimen had either no or minimal stress raisers, and the higher stresses observed in the narrow section were isolated from the gripping location. The findings contribute to understanding the relationship between standard geometry shapes, printing orientation, and the resulting tensile properties of 3D-printed polymer specimens.