  We simulate the bond and site percolation models on a simple-cubic lattice
with linear sizes up to L=512, and estimate the percolation thresholds to be
$p_c ({\rm bond})=0.248\,811\,82(10)$ and $p_c ({\rm site})=0.311\,607\,7(2)$.
By performing extensive simulations at these estimated critical points, we then
estimate the critical exponents $1/\nu =1.141\,0(15)$,
$\beta/\nu=0.477\,05(15)$, the leading correction exponent $y_i =-1.2(2)$, and
the shortest-path exponent $d_{\rm min}=1.375\,6(3)$. Various universal
amplitudes are also obtained, including wrapping probabilities, ratios
associated with the cluster-size distribution, and the excess cluster number.
We observe that the leading finite-size corrections in certain wrapping
probabilities are governed by an exponent $\approx -2$, rather than $y_i
\approx -1.2$.
