Most human tumors display chromosome-scale copy number alterations, and high levels of aneuploidy are frequently associated with advanced disease and poor patient prognosis. To examine the relationship between aneuploidy and cancer progression, we generated and analyzed a series of congenic human cell lines that harbor single extra chromosomes. We find that different aneuploidies can have distinct effects on invasive behavior: across 13 different cell lines, 12 trisomies suppressed invasiveness or were largely neutral, while a single trisomy increased metastatic behavior by triggering a partial epithelial-mesenchymal transition. In contrast, chromosomal instability, which can lead to the development of aneuploidy, uniformly suppressed cellular invasion. By analyzing genomic copy number and survival data from 10,133 cancer patients, we demonstrate that specific aneuploidies are associated with distinct clinical outcomes, and the acquisition of certain aneuploidies is in fact linked with a favorable prognosis. Thus, aneuploidy is not a uniform driver of malignancy, and different chromosome copy number changes can uniquely influence tumor progression. At the same time, the gain of a single chromosome is capable of inducing a profound cell state transition, underscoring how genomic plasticity can engender phenotypic plasticity and lead to the acquisition of enhanced metastatic properties.