Rest-frame ultraviolet (UV) emission lines offer the exciting possibility to directly image the gas around high-redshift galaxies with upcoming optical instruments. We use a suite of large, hydrodynamical simulations to predict the nature and detectability of emission lines from the intergalactic medium (IGM) at 2 ≤ z ≤ 5. The brightest emission comes from H i Lyα (1216 Å) and the strongest metal line, C iii (977), is about an order of magnitude fainter, although H i Lyα may be fainter if the gas is self-shielded to the UV background or if dust is important. The highest surface brightness regions for C iv (1548, 1551), Si iii (1207), Si iv (1393, 1403) and O vi (1032, 1038) are fainter than the brightest C iii by factors of a few. The N v (1239, 1243) and Ne viii (770, 780) lines, as well as He ii Hα (1640), are substantially weaker, but their maximum surface brightnesses still exceed 102 photon s−1 cm−2 sr−1 at z = 2 (for 2-arcsec pixels). Lower ionization lines typically arise in denser and colder gas that produces clumpier emission. The brightest H i Lyα emission arises exclusively in highly overdense gas, but the highest surface brightness emission from high-ionization metal lines traces a much wider range of overdensities. Bright metal-line emission traces gas with temperatures close to the peak of the corresponding emissivity curve. While H i Lyα, He ii Hα, C iii, Si iii and Si iv are excellent probes of cold accretion flows and the colder parts of outflows, C iv, N v, O vi and Ne viii are powerful tracers of the diffuse warm–hot IGM and galactic winds. A comparison of results from simulations with varying physical prescriptions demonstrates that the predictions for the brighter metal-line emission are robust to within factors of a few. Several rest-frame UV emission lines from the high-redshift IGM will become detectable in the near future, possibly starting with the Cosmic Web Imager, which is already operating on Palomar. The Multi Unit Spectroscopic Explorer, which will be commissioned in 2012 on the Very Large Telescope, and the proposed Keck Cosmic Web Imager have the potential to revolutionize studies of the interactions between high-redshift galaxies and their environment.