Conductance fluctuations in quantum wires are calculated numerically by a scattering-matrix formalism with Landauer's conductance formula. The fluctuations are not universal because they are strongly dependent on the system length. When many subbands are occupied, there appears the length region (called the universal region) longer than the mean free path and shorter than the localization length where the fluctuations are almost independent of the length. A crossover from one to two dimensions occurs when the broadening of one-dimensional subbands exceeds their separations. In the presence of a weak magnetic field, the universal region becomes wider and the fluctuations are reduced. In strong magnetic fields, the conductance becomes nearly quantized and the fluctuations become negligibly small due to the formation of edge states with an extremely long mean free path.