  We study bond percolation on several four-dimensional (4D) lattices,
including the simple (hyper) cubic (SC), the SC with combinations of nearest
neighbors and second nearest neighbors (SC-NN+2NN), the body-centered cubic
(BCC), and the face-centered cubic (FCC) lattices, using an efficient
single-cluster growth algorithm. For the SC lattice, we find $p_c =
0.1601312(2)$, which confirms previous results (based on other methods), and
find a new value $p_c=0.035827(1)$ for the SC-NN+2NN lattice, which was not
studied previously for bond percolation. For the 4D BCC and FCC lattices, we
obtain $p_c=0.074212(1)$ and 0.049517(1), which are substantially more precise
than previous values. We also find critical exponents $\tau = 2.3135(5)$ and
$\Omega = 0.40(3)$, consistent with previous numerical results and the recent
four-loop series result of Gracey [Phys. Rev. D 92, 025012, (2015)].
