Atomic transition probability measurements for 371 NiI lines in the UV through near-IR are reported. Branching fractions from data recorded using a Fourier transform spectrometer and a new echelle spectrograph are combined with published radiative lifetimes to determine these transition probabilities. Generally good agreement is found in comparisons to previously reported NiI transition probability measurements. Use of the new echelle spectrograph, independent radiometric calibration methods, and independent data analysis routines enable a reduction of systematic errors and overall improvement in transition probability uncertainty over previous measurements. The new NiI data are applied to high-resolution visible and UV spectra of the Sun and metal-poor star HD 84937 to derive new, more accurate Ni abundances. Lines covering a wide range of wavelength and excitation potential are used to search for non-LTE effects.