We present the first study of GALEX far-ultraviolet (FUV) luminosity functions of individual star-forming regions within a sample of 258 nearby galaxies spanning a large range in total stellar mass and star formation properties. We identify ~65000 star-forming regions (i.e. FUV sources), measure each galaxy's luminosity function, and characterize the relationships between the luminosity function slope ({alpha}) and several global galaxy properties. A final sample of 82 galaxies with reliable luminosity functions are used to define these relationships and represent the largest sample of galaxies with the largest range of galaxy properties used to study the connection between luminosity function properties and galaxy environment. We find that {alpha} correlates with global star formation properties, where galaxies with higher star formation rates and star formation rate densities ({Sigma}_SFR_) tend to have flatter luminosity function slopes. In addition, we find that neither stochastic sampling of the luminosity function in galaxies with low-number statistics nor the effects of blending due to distance can fully account for these trends. We hypothesize that the flatter slopes in high {Sigma}_SFR_ galaxies is due to higher gas densities and higher star formation efficiencies which result in proportionally greater numbers of bright star-forming regions. Finally, we create a composite luminosity function composed of star-forming regions from many galaxies and find a break in the luminosity function at brighter luminosities. However, we find that this break is an artefact of varying detection limits for galaxies at different distances.