We use the Herschel/PACS spectrometer to study the global and spatially resolved far-infrared (FIR) fine-structure line emission in a sample of 52 galaxies that constitute the SHINING survey. These galaxies include star-forming, active-galactic nuclei (AGNs), and luminous infrared galaxies (LIRGs). We find an increasing number of galaxies (and kiloparsec-size regions within galaxies) with low line-to-FIR continuum ratios as a function of increasing FIR luminosity (LFIR), dust infrared color, LFIR to molecular gas mass ratio (LFIR/Mmol), and FIR surface brightness ( FIR). The correlations between the C ii/FIR or O i/FIR ratios with FIR are remarkably tight (∼0.3 dex scatter over almost four orders of magnitude in FIR). We observe that galaxies with and FIR 1011 L kpc−2 tend to have weak fine-structure line-to-FIR continuum ratios, and that LIRGs with infrared sizes 1 kpc have line-to-FIR ratios comparable to those observed in typical star-forming galaxies. We analyze the physical mechanisms driving these trends in Paper II. The combined analysis of the C ii, N ii 122 m, and O iii 88 m lines reveals that the fraction of the C ii line emission that arises from neutral gas increases from 60% to 90% in the most active star-forming regions and that the emission originating in the ionized gas is associated with low-ionization, diffuse gas rather than with dense gas in H ii regions. Finally, we report the global and spatially resolved line fluxes of the SHINING galaxies to enable the comparison and planning of future local and high-z studies.