  We perform large scale finite-temperature Monte Carlo simulations of the
classical $e_g$ and $t_{2g}$ orbital models on the simple cubic lattice in
three dimensions. The $e_g$ model displays a continuous phase transition to an
orbitally ordered phase. While the correlation length exponent
$\nu\approx0.66(1)$ is close to the 3D XY value, the exponent $\eta \approx
0.15(1)$ differs substantially from O(N) values. At $T_c$ a U(1) symmetry
emerges, which persists for $T<T_c$ below a crossover length scaling as
$\Lambda \sim \xi^a$, with an unusually small $a\approx1.3$. Finally, for the
$t_{2g}$ model we find a {\em first order} transition into a low-temperature
lattice-nematic phase without orbital order.
