  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 (AGN), 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 ($L_{\mathrm{FIR}}$), dust infrared color,
$L_{\mathrm{FIR}}$ to molecular gas mass ratio
($L_{\mathrm{FIR}}/M_{\mathrm{mol}}$), and FIR surface brightness
($\Sigma_{\mathrm{FIR}}$). The correlations between the [CII]/FIR or [OI]/FIR
ratios with $\Sigma_{\mathrm{FIR}}$ are remarkably tight ($\sim0.3$ dex scatter
over almost four orders of magnitude in $\Sigma_{\mathrm{FIR}}$). We observe
that galaxies with $L_{\mathrm{FIR}}/M_{\mathrm{mol}} \gtrsim
80\,L_{\odot}\,M_{\odot}^{-1}$ and $\Sigma_{\mathrm{FIR}}\gtrsim10^{11}$
$L_{\odot}$ kpc$^{-2}$ tend to have weak fine-structure line-to-FIR continuum
ratios, and that LIRGs with infrared sizes $\gtrsim1$ 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 (Herrera-Camus
et al. 2018). The combined analysis of the [CII], [NII], and [OIII] lines
reveals that the fraction of the [CII] 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 HII 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.
