We present nearly simultaneous NuSTAR and XMM-Newton observations of the nearby (832 kpc) ultraluminous X-ray source (ULX) M33 X-8. M33 X-8 has a 0.3-10 keV luminosity of LX ~ 1.4 x 10^39 erg/s, near the boundary of the ultraluminous classification, making it an important source for understanding the link between typical Galactic X-ray binaries and ULXs. Past studies have shown that the 0.3-10 keV spectrum of X-8 can be characterized using an advection-dominated accretion disk model. We find that when fitting to our NuSTAR and XMM-Newton observations, an additional high-energy (>10 keV) Comptonization component is required, which allows us to rule out single advection-dominated disk and classical sub-Eddington models. With our new constraints, we analyze XMM-Newton data taken over the last 17 years to show that small (~30%) variations in the 0.3-10 keV flux of M33 X-8 result in spectral changes similar to those observed for other ULXs. The two most likely phenomenological scenarios suggested by the data are degenerate in terms of constraining the nature of the accreting compact object (i.e., black hole versus neutron star). We further present a search for pulsations using our suite of data; however, no clear pulsations are detected. Future observations designed to observe M33 X-8 at different flux levels across the full 0.3-30 keV range would significantly improve our constraints on the nature of this important source.