Imaging phantoms are used to calibrate and validate the performance of magnetic resonance imaging (MRI) systems. Many new materials have been developed for additive manufacturing (three-dimensional [3D] printing) processes that may be useful in the direct printing or casting of dimensionally accurate, anatomically accurate, patient-specific, and/or biomimetic MRI phantoms. The T-1, T-2, and T-2* spin relaxation times of polymer samples were tested to discover materials for use as tissue mimics and structures in MRI phantoms. This study included a cohort of polymer compounds that was tested in cured form. The cohort consisted of 101 standardized polymer samples fabricated from: two-part silicones and polyurethanes used in commercial casting processes; one-part optically cured polyurethanes used in 3D printing; and fused deposition thermoplastics used in 3D printing. The testing was performed at 3 T using inversion recovery, spin echo, and gradient echo sequences for T-1, T-2, and T-2*, respectively. T-1, T-2, and T-2* values were plotted with error bars to allow the reader to assess how well a polymer matches a tissue for a specific application. A correlation was performed between T-1, T-2, T-2* values and material density, elongation, tensile strength, and hardness. Two silicones, SI_XP-643 and SI_P-45, may be usable mimics for reported liver values; one silicone, SI_XP-643, may be a useful mimic for muscle; one silicone, SI_XP-738, may be a useful mimic for white matter; and four silicones, SI_P-15, SI_GI-1000, SI_GI-1040, and SI_GI-1110, may be usable mimics for spinal cord. Elongation correlated to T-2 (p = 0.0007), tensile strength correlated to T-1 (p = 0.002), T-2 (p = 0.0003), and T-2* (p = 0.003). The 80 samples not providing measurable signal with T-1, T-2, T-2* relaxation values too short to measure with the standard sequences, may be useful for MRI-invisible fixturing and medical devices at 3 T.