  The energy spectrum of magnetohydrodynamic turbulence attracts interest due
to its fundamental importance and its relevance for interpreting astrophysical
data. Here we present measurements of the energy spectra from a series of
high-resolution direct numerical simulations of MHD turbulence with a strong
guide field and for increasing Reynolds number. The presented simulations, with
numerical resolutions up to 2048^3 mesh points and statistics accumulated over
30 to 150 eddy turnover times, constitute, to the best of our knowledge, the
largest statistical sample of steady state MHD turbulence to date. We study
both the balanced case, where the energies associated with Alfv\'en modes
propagating in opposite directions along the guide field, E^+ and $E^-, are
equal, and the imbalanced case where the energies are different. In the
balanced case, we find that the energy spectrum converges to a power law with
exponent -3/2 as the Reynolds number is increased, consistent with
phenomenological models that include scale-dependent dynamic alignment. For the
imbalanced case, with E^+>E^-, the simulations show that E^- ~ k_{\perp}^{-3/2}
for all Reynolds numbers considered, while E^+ has a slightly steeper spectrum
at small Re. As the Reynolds number increases, E^+ flattens. Since both E^+ and
E^- are pinned at the dissipation scale and anchored at the driving scales, we
postulate that at sufficiently high Re the spectra will become parallel in the
inertial range and scale as E^+ ~ E^- ~ k_{\perp}^{-3/2}. Questions regarding
the universality of the spectrum and the value of the "Kolmogorov constant" are
discussed.
