We report the application of supervised machine learning to the automated classification of lipid-droplets in label-free, quantitative-phase images. By comparing various machine learning methods that are publicly available and commonly used in biomedical imaging and remote sensing, we found convolutional neural networks to outperform others, both quantitatively and qualitatively. We describe our imaging approach, the implementation of all machine learning methods that we compared, and their performance in computational requirements, training resource needs, and accuracy. Overall, our results indicate that quantitative-phase imaging coupled to machine learning enables accurate lipid droplet classification in single living cells. As such, the present paradigm presents an excellent replacement candidate of the more common fluorescent and Raman imaging modalities by enabling label-free, ultra-low phototoxicity and deeper insight into the thermodynamics of metabolism at the single-cell level.