The homoleptic binuclear compound Fe-2(CO)(9) is well characterized experimentally, although there has been some discussion as to the nature of the iron-iron bond, which is at most a single bond. In this research, we consider homoleptic iron carbonyls that satisfy the 18-electron rule but may have formal double Fe-2(CO)(8) (seven distinct structures), triple Fe-2(CO)(7) (three distinct structures), and even quadruple Fe-2(CO)(6) (seven distinct structures) iron-iron bonds. These novel structures are characterized in terms of their equilibrium geometries, thermochemistry, and vibrational frequencies. The range of predicted iron-iron distances is remarkable, from 2.52 Angstrom for the known Fe-2(CO)(9) to 2.00 Angstrom for the unbridged quadruple bond species Fe-2(CO)(6). The lowest energy structure of Fe-2(CO)(7) is a distorted unbridged C-s symmetry structure with iron-iron separation 2.23 Angstrom. This is followed energetically by the tribridged structure with bond distance 2.21 Angstrom, and finally by the monobridged structure with iron-iron distance 2.13 Angstrom. The latter structure is consistent with an Fe=Fe triple bond, but is not a genuine minimum. For Fe-2(CO)(6) the lowest energy structure is the distorted dibridged structure with perhaps a weak Fe=Fe double bond. However, the unbridged Fe-2(CO)(6) structure with an iron-iron bond distance of 2.00 Angstrom (suggesting a quadruple bond) is also a genuine minimum, The unsaturated structures Fe-2(CO)(8) and Fe-2(CO)(7), are thermodynamically resistant to CO removal. The iron-iron linkages are also analyzed in terms of contributions from the different vibrational potential energy distributions. A clear Badger's Rule correlation between Fe-Fe vibrational frequency and bond distance is established. Prospects for the synthesis of these and related diiron compounds are discussed in some detail. The most promising routes to preparation of these fascinating species would appear to be matrix isolation or iron vapor synthesis.