  We present analytical and numerical results for the effect of Rashba
spin-orbit coupling on band structure, transport, and interaction effects in
quantum wires when the spin precession length is comparable to the wire width.
In contrast to the weak-coupling case, no common spin-quantization axis can be
defined for eigenstates within a single-electron band. The situation with only
the lowest spin-split subbands occupied is particularly interesting because
electrons close to Fermi points of the same chirality can have approximately
parallel spins. We discuss consequences for spin-dependent transport and
effective Tomonaga-Luttinger descriptions of interactions in the quantum wire.
