[abridged] We present far-infrared spectroscopic observations of PMS stars taken with Herschel/PACS as part of the DIGIT key project. The sample includes 22 Herbig AeBe and 8 T Tauri sources. Multiple atomic fine structure and molecular lines are detected at the source position: [OI], [CII], CO, OH, H_2O, CH^+. The most common feature is the [OI] 63micron line detected in almost all of the sources followed by OH. In contrast with CO, OH is detected toward both Herbig AeBe groups (flared and non-flared sources). An isothermal LTE slab model fit to the OH lines indicates column densities of 10^13 < N_OH < 10^16 cm^-2, emitting radii 15 < r < 100 AU and excitation temperatures 100 < T_ex < 400 K. The OH emission thus comes from a warm layer in the disk at intermediate stellar distances. Warm H_2O emission is detected through multiple lines toward the T Tauri systems AS 205, DG Tau, S CrA and RNO 90 and three Herbig AeBe systems HD 104237, HD 142527, HD 163296 (through line stacking). Overall, Herbig AeBe sources have higher OH/H_2O abundance ratios across the disk than do T Tauri disks, from near- to far-infrared wavelengths. Far-infrared CH^+ emission is detected toward HD 100546 and HD 97048. The slab model suggests moderate excitation (T_ex ~ 100 K) and compact (r ~ 60 AU) emission in the case of HD 100546. The [CII] emission is spatially extended in all sources where the line is detected. This suggests that not all [CII] emission is associated with the disk and that there is a substantial contribution from diffuse material around the young stars. The flux ratios of the atomic fine structure lines are consistent with a disk origin for the oxygen lines for most of the sources.
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