We investigate the spin dynamics of high-mobility two-dimensional electrons in GaAs/AlGaAs quantum wells grown along the [001] and [110] directions by time-resolved Faraday rotation at low temperatures. In measurements on the (001)-grown structures without external magnetic fields, we observe coherent oscillations of the electron-spin polarization about the effective spin-orbit field. In nonquantizing magnetic fields applied normal to the sample plane, the cyclotron motion of the electrons rotates the effective spin-orbit field. This rotation leads to fast oscillations in the spin polarization about a nonzero value and a strong increase in the spin dephasing time in our experiments. These two effects are absent in the (110)-grown structure due to the different symmetry of its effective spin-orbit field. The measurements are in excellent agreement with our theoretical model.