The concept of exchange energy is a distinctive feature of quantum-mechanical models of many-electron systems. Usually, only exchange interactions involving spin-1/2 fermions (electrons) are considered. We deduce and examine Hartree-Fock exchange energy formulas and exchange density functionals for fermions of arbitrary spin quantum number. The explicit spin-dependence provides illuminating insights into the meaning of exchange interactions, correspondence principle, self-interaction error, and other concepts of electronic structure theory.