  Evidence is mounting that some Ultra-luminous X-ray sources (ULXs) may
contain accreting intermediate-mass black holes (IMBHs). We review the current
observational evidence for IMBH-ULXs. While low-luminosity ULXs with L_X <~
10^39.5 erg/s (assuming isotropic emission) are consistent with mildly X-ray
beamed high-mass X-ray binaries, there are a considerable number of ULXs with
larger X-ray luminosities that are not easily explained by these models. Recent
high-S/N XMM X-ray spectra are showing an increasing number of ULXs with ``cool
disks'' -- accretion disks with multi-color blackbody inner disk temperatures
kT_in ~ 0.1-0.2 keV, consistent with accreting IMBHs. Optical emission-line
studies of ULX nebulae provide useful measurements of X-ray energetics, and can
thus determine if the X-rays are emitted isotropically. Analysis of an optical
spectrum of the Ho II ULX nebulae implies an X-ray energy source with ~10^40
erg/s is present, suggesting an isotropically-emitting IMBH. The spatial
coincidence of ULXs with dense star clusters (young clusters and globular
clusters) suggests that IMBHs formed in these clusters could be the compact
objects in the associated ULXs. Quasi-periodic oscillations and frequency
breaks in XMM power-density spectra of ULXs also suggest that the black hole
masses are more consistent with IMBHs than stellar-mass black holes. Since
_all_ of these ULXs with evidence for IMBHs are high-luminosity ULXs, i.e., L_X
>~ 10^40 ergs, we suggest that this class of ULXs is generally powered by
accreting IMBHs.
