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This paper discusses the results of an experimental study aimed at evaluating the influence of the vertical ground motion component on the seismic performance of unreinforced brick-masonry buildings. The research was motivated by post-earthquake observations of significant structural damage in the vicinity of the fault, where horizontal and vertical ground motions are often strong and synchronized. Vertical accelerations can fluctuate gravity loads, which control the in-plane lateral load capacity of masonry piers and affect the out-of-plane overturning stability of thin walls. Such phenomena seem not to be sufficiently explained in existing literature, while experimental evidence is undoubtedly missing. Here, the damage potential of vertical accelerations was investigated through a series of multidirectional shake-table tests on full-scale structures under simulated near-source ground motions of increasing intensity. The experiments comprised three nominally identical building specimens subjected to the principal horizontal component alone, the horizontal component combined with the vertical one, and the full three-component ground motion. The buildings included structural/nonstructural elements (e.g., gables, chimneys, and parapets) sensitive to gravity load variations due to their low axial loads. Two different sets of three-component earthquake records were employed to assess the effects of both tectonic and induced seismicity scenarios. Overall, the vertical earthquake motion did not cause appreciable differences in the behavior of the buildings. Any influence on the strength and peak response of structural/nonstructural walls was marginal and non-systematic. Data and observations from these experiments add substantially to our understanding of the vertical acceleration effects on masonry structures.