We systematically investigate the effects of geometrical assumptions in one-dimensional (1D) models of coronal loops. Many investigations of coronal loops have been based on restrictive assumptions, including symmetry in the loop shape and heating profile, and a uniform cross-sectional area. Starting with a solution for a symmetric uniform-area loop with uniform heating, we gradually relax these restrictive assumptions to consider the effects of nonuniform area, nonuniform heating, a nonsymmetric loop shape, and nonsymmetric heating, to show that the character of the solutions can change in important ways. We find that loops with nonuniform cross-sectional area are more likely to experience thermal nonequilibrium, and that they produce significantly enhanced coronal emission, compared with their uniform-area counterparts. We identify a process of incomplete condensation in loops experiencing thermal nonequilibrium during which the coronal parts of loops never fully cool to chromospheric temperatures. These solutions are characterized by persistent siphon flows. Their properties agree with observations (Lionello et al.) and may not suffer from the drawbacks that led Klimchuk et al. to conclude that thermal nonequilibrium is not consistent with observations. We show that our 1D results are qualitatively similar to those seen in a three-dimensional model of an active region. Our results suggest that thermal nonequilibrium may play an important role in the behavior of coronal loops, and that its dismissal by Klimchuk et al., whose model suffered from some of the restrictive assumptions we described, may have been premature.