We present an analysis of ASCA spatially resolved spectroscopic data for a nearly complete sample of bright clusters with redshifts between 0.04 and 0.09. Together with several clusters analyzed elsewhere using the same method, this sample consists of 30 objects with T e ∼ > 3.5 keV for which we obtained projected temperature profiles and, when possible, crude two-dimensional temperature maps. All clusters, with the possible exception of a few with insufficiently accurate data, are found to be nonisothermal with spatial temperature variations (apart from cooling flows) by a factor of 1.3-2. ASCA temperature maps for many clusters reveal merger shocks. The most notable of these are A754, A2065, A3558, A3667, and Cygnus A; merging can also be inferred with lower confidence from the A85, A119, and A2657 temperature maps and from the A3395 and Triangulum Australis entropy maps. About half of the sample shows signs of merging; in about 60% of the sample, we detect cooling flows. Nearly all clusters show a significant radial temperature decline at large radii. For a typical 7 keV cluster, the observed temperature decline between 1 and 6 X-ray core radii (0.15 and 0.9 h −1 Mpc) can be approximately quantified by a polytropic index of 1.2-1.3. Assuming such a polytropic temperature profile and hydrostatic equilibrium, the gravitating mass within 1 and within 6 core radii is approximately 1.35 and 0.7 times the isothermal β-model estimates, respectively.Most interestingly, we find that temperature profiles, excluding those for the most asymmetric clusters, appear remarkably similar when the temperature is plotted against radius in units of the estimated virial radius. We compare the composite temperature profile to a host of published hydrodynamic simulations. The observed profiles appear steeper than predictions of most Lagrangian simulations (Evrard, Metzler, & Navarro 1996;Eke, Navarro, & Frenk 1997). The predictions for Ω = 1 cosmological models are most discrepant, while models with low Ω are closer to our data. We note, however, that at least one Ω = 1 Lagrangian simulation (Katz & White 1993) and the recent high-resolution Eulerian simulation (Bryan & Norman 1997) produced clusters with temperature profiles similar to or steeper than those observed. Our results thus provide a new constraint for adjusting numerical simulations and, potentially, discriminating among models of cluster formation.