Precision measurements of the electron component in the cosmic radiation provide important information about the origin and propagation of cosmic rays in the Galaxy. Here we present new results regarding negatively charged electrons between 1 and 625 GeV performed by the satellite-borne experiment PAMELA. This is the first time that cosmic-ray electrons have been identified above 50 GeV. The electron spectrum can be described with a single power law energy dependence with spectral index -3.18 +- 0.05 above the energy region influenced by the solar wind (> 30 GeV). No significant spectral features are observed and the data can be interpreted in terms of conventional diffusive propagation models. However, the data are also consistent with models including new cosmic-ray sources that could explain the rise in the positron fraction.