We present measurements of branching fractions and charge asymmetries for six B -meson decay modes with an η or η ′ meson in the final state. The data sample corresponds to 232 × 10 6 B ¯¯¯ B pairs collected with the BABAR detector at the PEP-II asymmetric-energy e + e − B Factory at SLAC. We measure the branching fractions (in units of 10 − 6 ): B ( B + → η π + ) = 5.1 ± 0.6 ± 0.3 , B ( B + → η K + ) = 3.3 ± 0.6 ± 0.3 , B ( B 0 → η K 0 ) = 1.5 ± 0.7 ± 0.1 ( < 2.5 at 90% C.L.), B ( B + → η ρ + ) = 8.4 ± 1.9 ± 1.1 , B ( B 0 → η ω ) = 1.0 ± 0.5 ± 0.2 ( < 1.9 at 90% C.L.), and B ( B + → η ′ π + ) = 4.0 ± 0.8 ± 0.4 , where the first uncertainty is statistical and second systematic. For the charged modes we also determine the charge asymmetries, all found to be compatible with zero.