The ROSAT EUV all-sky survey was conducted with the UK Wide Field Camera (WFC) over the six-month period 1990 July to 1991 January, in two `colours' using broadband filters to define wavebands centred at about 100 and 140 Å. We present EUV luminosity functions (LFs) for volume-limited samples of stars selected from the Third Catalogue of Nearby Stars (CNS3), using distance limits of 25 and 16 pc for the F-K and M stars respectively. LFs have been computed for both single stars and spectroscopic binaries of each spectral type in both of the WFC survey passbands. The LFs may be adequately described by power laws and are sufficiently flat that the stellar number-flux relations (`log N - log S') will be heavily influenced by the higher luminosity objects. Spectroscopic binaries have higher mean EUV luminosity and flatter slope than single stars and, indeed, the high-luminosity tail apparent in the G-star LF can be almost entirely attributed to spectroscopic binaries, the majority of which are RS CVn systems. A comparison with earlier Einstein Observatory (soft X-ray) results shows that there is broad agreement for the mean luminosities of F, G and K stars. Recently published Einstein results for M stars are also consistent with the EUV LFs, though earlier Einstein studies indicated much higher mean luminosities. This provides an explanation as to why the EUV log N - log S, contrary to pre-launch predictions, is not dominated by M stars. Comparison of log N - log S distributions predicted from our EUV LFs with those of late-type stars in the WFC Bright Source Catalogue (BSC), sampling EUV-bright stars over a larger distance range than our CNS3 study, shows an excess of K stars in BSC relative to the CNS3 sample. Most of these objects have recently been identified as active stars, and may well constitute a `yellow-star' excess similar to that found in Einstein X-ray surveys.