The coronal lines that are observable in the Hinode EUV Imaging Spectrometer (EIS) wavelengths are assessed with new atomic data that have recently become available for a range of important ions. EIS spectral lines are identified based on their spatial variation across different solar regions, their wavelengths, and their intensities. Two off-limb observations are presented, one above an active region, and one in the quiet Sun. The spectra are relatively free of low-temperature lines. Accurate wavelengths and intensities are provided. The observed and predicted line intensities generally agree excellently, once blending is taken into account. The main diagnostics available for measuring the electron density of the solar corona using EIS are highlighted with the use of the emissivity ratio technique. Densities obtained from different ions agree excellently. Most of the previous identifications are confirmed. A considerable number of weaker lines still await identification, however. The approximate formation temperature of the main unidentified lines is provided to aid the identification process. The EIS radiometric calibration appears to be in need of revision. A new quiet-Sun argon/iron relative abundance of 0.16, in line with Galactic measurements, is found. The abundances of sulphur and argon in the "background" unresolved active region emission are found to be lower by a factor of about two at 1.5 MK, and even lower at 3 MK.