Wigner crystals (WCs) are electronic phases peculiar to low-density systems, particularly in the uniform electron gas. Since its introduction in the early twentieth century, this model has remained essential to many aspects of electronic structure theory and condensed-matter physics. Although the (lowest-energy) ground-state WC (GSWC) has been thoroughly studied, the properties of excited-state WCs (ESWCs) are basically unknown. To bridge this gap, we present a well-defined procedure to obtain an entire family of ESWCs in a one-dimensional electron gas using a symmetry-broken mean-field approach. While the GSWC is a commensurate crystal (i.e., the number of density maxima equals the number of electrons), these ESWCs are incommensurate crystals exhibiting more or less maxima. Interestingly, they are lower in energy than the (uniform) Fermi fluid state. For some of these ESWCs, we have found asymmetrical band gaps, which would lead to anisotropic conductivity. These properties are associated with unusual characteristics in their electronic structure.