We review direct force measurements on a broad class of hydrophobic and hydrophilic surfaces. These measurements have enabled the development of a general interaction potential per unit area, W(D) = -2γ(i)Hy exp(-D/D(H)) in terms of a nondimensional Hydra parameter, Hy, that applies to both hydrophobic and hydrophilic interactions between extended surfaces. This potential allows one to quantitatively account for additional attractions and repulsions not included in the well-known combination of electrostatic double layer and van der Waals theories, the so-called Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The interaction energy is exponentially decaying with decay length D(H) ≈ 0.3-2 nm for both hydrophobic and hydrophilic interactions, with the exact value of D(H) depending on the precise system and conditions. The pre-exponential factor depends on the interfacial tension, γ(i), of the interacting surfaces and Hy. For Hy > 0, the interaction potential describes interactions between partially hydrophobic surfaces, with the maximum hydrophobic interaction (i.e., two fully hydrophobic surfaces) corresponding to Hy = 1. Hydrophobic interactions between hydrophobic monolayer surfaces measured with the surface forces apparatus (SFA) are shown to be well described by the proposed interaction potential. The potential becomes repulsive for Hy < 0, corresponding to partially hydrophilic (hydrated) interfaces. Hydrated surfaces such as mica, silica, and lipid bilayers are discussed and reviewed in the context of the values of Hy appropriate for each system.