We present the results of a complete survey, at extreme-ultraviolet (EUV) wavelengths (58-234 Angstrom), of the high Galactic latitude (\b\ greater than or equal to 20 degrees) planetary nebulae (PNs) with at least one determination of the distance within 1 kpc of the Sun. The sample comprises 27 objects observed during the Extreme Ultraviolet Explorer (EUVE) all-sky survey and represents the majority of PN likely to be accessible at EUV wavelengths. Six PNs (NGC 246, NGC 1360, K1-16, LoTr 5, NGC 4361, and NGC 3587) were detected in the shortest EUV band (58-174 Angstrom). A seventh PN (NGC 6853), not included in the sample, was also detected during the survey. The emission is consistent in all cases with that of a point source and therefore most probably originates from the PN central star. Accurate EUV count rates or upper limits in the two shorter EUVE bands (centered at approximate to 100 and 200 Angstrom) are given for all the sources in the sample. NGC 4361 and NGC 3587 are reported here for the first time as sources of EUV radiation. As might be expected, attenuation by the interstellar medium dominates the PN distribution in the EUV sky.