High-energy electrons have been measured systematically in a low-altitude (520¿675 km), nearly polar (inclination=82¿) orbit by sensitive instruments onboard the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX). Count rate channels with electron energy thresholds ranging from 0.4 MeV to 3.5 MeV in three different instruments have been used to examine relativistic electron variations as a function of L-shell parameter and time. A long run of essentially continuous data (July 1992--July 1993) shows substantial acceleration of energetic electrons throughout much of the magnetosphere on rapid time scales. This acceleration appears to be due to solar wind velocity enhancements and is surprisingly large in that the radiation belt ''slot'' region often is filled temporarily and electron fluxes are strongly enhanced even at very low L values (L~2). A superposed epoch analysis shows that electron fluxes rise rapidly for 2.5≲L≲5. These increases occur on a time scale of order 1--2 days and are most abrupt for L-values near 3. The temporal decay rate of the fluxes is dependent on energy and L-value and may be described by J=Ke-t/t0 with t0≈5--10 days. Thus, these results suggest that the Earth's magnetosphere is a cosmic electron accelerator of substantial strength and efficiency.