We present a density-functional theory for binary mixtures of amphiphiles with solvent, placing particular emphasis on the structure and free energy of stable and metastable clusters of amphiphiles in dilute solution. These correspond to micelles (complexes of amphiphiles with the solvophobic groups clustered in the interior) and vesicles (spherical complexes with bilayer membranes of amphiphiles with solvent both inside and outside the membrane shell). Saddle points that connect these states are also explored to study the nucleation behavior of these systems. Our approach is applicable to both strong and weak amphiphiles, and can be readily extended to the full ternary phase equilibria characteristic of microemulsions.