Astronomers are always anxious to push their observations to the limit-basing results on objects at the detection threshold, spectral features barely stronger than the noise, or photometry in very crowded regions. In this paper we present a careful analysis of photometry in crowded regions and show how image blending affects the results and interpretation of such data. Although this analysis is specifically for our NICMOS observations in M31, the techniques we develop can be applied to any imaging data taken in crowded fields; we show how the effects of image blending will limit even the Next Generation Space Telescope. We have obtained HST-NICMOS observations of five of M31's most metal-rich globular clusters. These data allow photometry of individual stars in the clusters and their surrounding fields. However, to achieve our goals-obtain accurate luminosity functions to compare with their Galactic counterparts, determine metallicities from the slope of the giant branch, identify long-period variables, and estimate ages from the AGB tip luminosity-we must be able to disentangle the true properties of the population from the observational effects associated with measurements made in very crowded fields. We thus use three different techniques to analyze the effects of crowding on our data, including the insertion of artificial stars (traditional completeness tests) and the creation of completely artificial clusters. These computer simulations are used to derive threshold- and critical-blending radii for each cluster, which determine how close to the cluster center reliable photometry can be achieved. The simulations also allow us to quantify and correct for the effects of blending on the slope and width of the RGB at different surface brightness levels. We then use these results to estimate the limits blending will place on future space-based observations. Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy (AURA), Inc., for NASA under contract NAS 5-26555.