  (Abridged) We revisit the question of the nature of ULXs through a detailed
investigation of their spectral shape, using the highest quality X-ray data
available in the XMM-Newton public archives. We confirm that simple spectral
models commonly used for the analysis and interpretation of ULXs (power-law
continuum and multi-colour disc blackbody models) are inadequate in the face of
such high quality data. Instead we find two near ubiquitous features in the
spectrum: a soft excess and a roll-over in the spectrum at energies above 3keV.
We investigate a range of more physical models to describe these data. We find
that disc plus Comptonised corona models fit the data well, but the derived
corona is cool, and optically thick (tau ~ 5-30). We argue that these observed
disc temperatures are not a good indicator of the black hole mass as the
powerful, optically thick corona drains energy from the inner disc, and
obscures it. We estimate the intrinsic (corona-less) disc temperature, and
demonstrate that in most cases it lies in the regime of stellar mass black
holes. These objects have spectra which range from those similar to the highest
mass accretion rate states in Galactic binaries, to those which clearly have
two peaks, one at energies below 1 keV (from the outer, unComptonised disc) and
one above 3 keV (from the Comptonised, inner disc). However, a few ULXs have a
significantly cooler corrected disc temperature; we suggest that these are the
most extreme stellar mass black hole accretors, in which a massive wind
completely envelopes the inner disc regions, creating a cool photosphere. We
conclude that ULXs provide us with an observational template for the transition
between Eddington and super-Eddington accretion flows, with the latter
occupying a new ultraluminous accretion state.
