Laser-driven, quasimonoenergetic electron beams of up to approximately 200 MeV in energy have been observed from steady-state-flow gas cells. These beams emitted within a low-divergence cone of 2.1+/-0.5 mrad FWHM display unprecedented shot-to-shot stability in energy (2.5% rms), pointing (1.4 mrad rms), and charge (16% rms) owing to a highly reproducible gas-density profile within the interaction volume. Laser-wakefield acceleration in gas cells of this type provides a simple and reliable source of relativistic electrons suitable for applications such as the production of extreme-ultraviolet undulator radiation.