During metastasis, cancer cells are exposed to various three-dimensional microstructures within the body, but the relationship between cancer migration and three-dimensional geometry remain largely unclear. Here, such geometric effects on cancerous cells were investigated by characterizing the motility of various cancer cell types on microgroove-based topographies made of polydimethylsiloxane (PDMS), with particular emphasis on distinguishing cancerous and non-cancerous epithelial cells, as well as understanding the underlying mechanism behind such differences. The 90-degree walls enhanced motility for all cell lines, but the degrees of enhancements were less pronounced for the cancerous cells. Interestingly, while the non-cancerous epithelial cell types conformed to the three-dimensional geometrical cues and migrated along the walls, the cancerous cell types exhibited a unique behavior of climbing upright walls, and this was associated with the inability to form stable, polarized actin cytoskeleton along the walls of the microgrooves. Furthermore, when non-cancerous epithelial cell lines were altered to different levels of polarization capabilities and cancer malignancy or treated with inhibitory drugs, their three-dimensional geometry-dependent motility approached those of cancerous cell lines. Overall, the results suggest that cancerous cells may gradually lose geometrical recognition with increasing cancer malignancy, allowing them to roam freely ignoring three-dimensional geometrical cues during metastasis.