Even genetically identical cells have heterogeneous properties because of stochasticity in gene or protein expression. Single cell techniques that assay heterogeneous properties would be valuable for basic science and diseases like cancer, where accurate estimates of tumor properties is critical for accurate diagnosis and grading. Cell morphology is an emergent outcome of many cellular processes, potentially carrying information about cell properties at the single cell level. Here we study whether morphological parameters are sufficient for classification of single cells, using a set of 15 cell lines, representing three processes: (i) the transformation of normal cells using specific genetic mutations; (ii) metastasis in breast cancer and (iii) metastasis in osteosarcomas. Cellular morphology is defined as quantitative measures of the shape of the cell and the structure of the actin. We use a toolbox that calculates quantitative morphological parameters of cell images and apply it to hundreds of images of cells belonging to different cell lines. Using a combination of dimensional reduction and machine learning, we test whether these different processes have specific morphological signatures and whether single cells can be classified based on morphology alone. Using morphological parameters we could accurately classify cells as belonging to the correct class with high accuracy. Morphological signatures could distinguish between cells that were different only because of a different mutation on a parental line. Furthermore, both oncogenesis and metastasis appear to be characterized by stereotypical morphology changes. Thus, cellular morphology is a signature of cell phenotype, or state, at the single cell level.