We report Herschel SPIRE (250, 350, and 500 μm) detections of 32 quasars with redshifts 0.5 <=z < 3.6 from the Herschel Multi-tiered Extragalactic Survey (HerMES). These sources are from a MIPS 24 μm flux-limited sample of 326 quasars in the Lockman Hole Field. The extensive multi-wavelength data available in the field permit construction of the rest-frame spectral energy distributions (SEDs) from ultraviolet to the mid-infrared for all sources, and to the far-infrared (FIR) for the 32 objects. Most quasars with Herschel FIR detections show dust temperatures in the range of 25-60 K, with a mean of 34 K. The FIR luminosities range from 1011.3 to 1013.5 L &sun;, qualifying most of their hosts as ultra- or hyper-luminous infrared galaxies. These FIR-detected quasars may represent a dust-rich population, but with lower redshifts and fainter luminosities than quasars observed at ~1 mm. However, their FIR properties cannot be predicted from shorter wavelengths (0.3-20 μm, rest frame), and the bolometric luminosities derived using the 5100 Å index may be underestimated for these FIR-detected quasars. Regardless of redshift, we observed a decline in the relative strength of FIR luminosities for quasars with higher near-infrared luminosities.