We investigate the stability and thermal motion of optically trapped nanowires, with aspect ratios in the range 10-100. A simple analytical model is used to determine qualitative features of the system, assuming that the nanowire is weakly scattering and the incident beam is paraxial. As expected, the model predicts that the nanowire will align with the beam axis. In this configuration the translational stiffness coefficients of the trap approach their limiting values for long nanowires like O(L(-3)), where L is the nanowire length, the limit for the stiffness parallel to the beam axis being zero. The rotational stiffness coefficients vary more slowly, according to O(L(-1)). Also, it is predicted that defocusing decreases the translational stiffness perpendicular to the beam, while increasing rotational stiffness. These findings are reinforced by comparison with rigorous electromagnetic calculations which additionally reveal the effects of radiation pressure and finite scattering. A strong polarization effect is observed in the numerical simulations and coupled translational and rotational motions arise which influence the trap stability. The use of nanowire traps for force sensing is discusse.