Using first-principles GW plus Bethe-Salpeter equation calculations, we identify anomalously strong excitonic effects in several vacancy-ordered double perovskites Cs2MX6 (M = Ti, Zr; X = I, Br). Giant exciton binding energies about 1 eV are found in these moderate-gap, inorganic bulk semiconductors, pushing the limit of our understanding of electron-hole (e-h) interaction and exciton formation in solids. Not only are the exciton binding energies extremely large compared with any other moderate-gap bulk semiconductors, but they are also larger than typical 2D semiconductors with comparable quasiparticle gaps. Our calculated lowest bright exciton energy agrees well with the experimental optical band gap. The low-energy excitons closely resemble the Frenkel excitons in molecular crystals, as they are highly localized in a single [MX6]2- octahedron and extended in the reciprocal space. The weak dielectric screening effects and the nearly flat frontier electronic bands, which are derived from the weakly bonded [MX6]2- units, together explain the significant excitonic effects. Spin-orbit coupling effects play a crucial role in red-shifting the lowest bright exciton by mixing up spin-singlet and spin-triplet excitons, while exciton-phonon coupling effects have minor impacts on the strong exciton binding energies.