Overall, our study provides detailed fundamental information on the formation of metal-water interfaces encountered in several applications in electrochemistry, catalysis, and materials science. Our results show that the interface formation is driven by both energetic and entropic contributions. For the most strongly binding metals, Pt and Rh, the water adsorption energy dominates the formation thermodynamics while on slightly less binding metals, Pd and Ag, both entropic and energetic contributions are sizable. Our results also show that both highly structured (Rh and Pt) and unstructured (Au) interfacial water layers lead to small interfacial entropy contributions while the highest interfacial water entropies are observed for modestly ordered water layers (Ag and Pd). The entropy analysis shows that interfacial water has higher entropy than bulk water. The obtained results show that metal-water interface formation thermodynamics cannot be described using adsorption energies and the water structures alone because entropy arises mainly from the dynamics of the low frequency modes of translation and rotation.