Domain orientations in thin films of lamellar copolymers are evaluated as a function of copolymer architecture, film thickness, and processing conditions. Two copolymer architectures are considered: An AB diblock of poly(styrene-b-methyl methacrylate) and an ABA triblock of poly(methyl methacrylate-b-styrene-b-methyl methacrylate). All films are cast on substrates that are energetically neutral with respect to the copolymer constituents. Film structures are evaluated with optical microscopy, atomic force microscopy, and grazing-incidence small-angle X-ray scattering. For AB diblock copolymers, the domain orientations are very sensitive to film thickness, annealing temperature, and imperfections in the "neutral" substrate coating: Diblock domains are oriented perpendicular to the substrate when annealing temperature is elevated (>= 220 degrees C) and defects in the substrate coating are minimized; otherwise, parallel or mixed parallel/perpendicular domain orientations are detected for most film thicknesses. For ABA triblock copolymers, the perpendicular domain orientation is stable for all the film thicknesses and processing conditions that were studied. The orientations of diblock and triblock copolymers are consistent with recent works that consider architectural effects when calculating the copolymer surface tension (Macromolecules 2006, 39, 9346 and Macromolecules 2010, 43, 1671). Significantly, the data demonstrate that triblocks are easier to process for applications in nanopatterning-in particular, when high-aspect-ratio nanostructures are required. However, both diblock and triblock films contain a high density of "tilted" or bent domains, and these kinetically trapped defects should be minimized for most patterning applications.