Forbidden Ni II and Fe II emission in a sample of H II regions, circumstellar nebulae, Seyfert galaxies, and supernova remnants is studied using new atomic data. Electron densities and temperatures determined with [Ni II], [Fe II], and [O I] indicate considerably different conditions than those obtained with line ratios of other species. Strong [Fe II] to [O I] and [Fe II] to [Ni II] correlations can be established. Models of electron impact excitation and fluorescence excitation by UV continuum of [Ni II] and [Fe II] lines show that fluorescence of [Fe II] lines may not be important, thus constraining the dominant emitting region to the high-density partially ionized zones, while for [Ni II] lines fluorescence excitation from low-density fully ionized zones in the Orion nebula and circumstellar nebulae could extend the emitting region over that of [Fe II]. Fluorescence excitation of these lines in supernova remnants seems unimportant. Abundance ratios Fe/O and Ni/Fe are estimated for Orion and some supernova remnants. It is found that the Fe/O ratios in all cases are within a factor of 2 of the solar value. The Ni/Fe ratio in supernova remnants seems to be considerably greater than solar.