We observed a sample of 20 representative Herbig Ae/Be stars and five A-type debris discs with PACS onboard of Herschel. The observations were done in spectroscopic mode, and cover far-IR lines of [OI], [CII], CO, CH+, H2O and OH. We have a [OI]63 micron detection rate of 100% for the Herbig Ae/Be and 0% for the debris discs. [OI]145 micron is only detected in 25%, CO J=18-17 in 45% (and less for higher J transitions) of the Herbig Ae/Be stars and for [CII] 157 micron, we often found spatially variable background contamination. We show the first detection of water in a Herbig Ae disc, HD 163296, which has a settled disc. Hydroxyl is detected as well in this disc. CH+, first seen in HD 100546, is now detected for the second time in a Herbig Ae star, HD 97048. We report fluxes for each line and use the observations as line diagnostics of the gas properties. Furthermore, we look for correlations between the strength of the emission lines and stellar or disc parameters, such as stellar luminosity, UV and X-ray flux, accretion rate, PAH band strength, and flaring. We find that the stellar UV flux is the dominant excitation mechanism of [OI]63 micron, with the highest line fluxes found in those objects with a large amount of flaring and greatest PAH strength. Neither the amount of accretion nor the X-ray luminosity has an influence on the line strength. We find correlations between the line flux of [OI]63 micron and [OI]145 micron, CO J = 18-17 and [OI]6300 AA, and between the continuum flux at 63 micron and at 1.3 mm, while we find weak correlations between the line flux of [OI]63 micron and the PAH luminosity, the line flux of CO J = 3-2, the continuum flux at 63 micron, the stellar effective temperature and the Brgamma luminosity. (Abbreviated version)
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