Five well-known Zr-based alloys of the systems Zr–Cu–Al–(Ni–Nb, Ni–Ti, Ag) (Cu = 15.4–36 at.%) with the highest glass-forming ability were comparatively analyzed regarding their pitting corrosion resistance and repassivation ability in a chloride-containing solution. Potentiodynamic polarization measurements were conducted in the neutral 0.01 M Na2SO4 + 0.1 M NaCl electrolyte and local corrosion damages were subsequently investigated with high resolution scanning electron microscopy (HR-SEM) coupled with energy dispersive x-ray spectroscopy (EDX). Both pitting and repassivation potential correlate with the Cu concentration, i.e., those potentials decrease with increasing Cu content. Pit morphology is not composition dependent: while initially hemispherical pits then develop an irregular shape and a porous rim. Corrosion products are rich in Cu, O, and often Cl species. A combination of low Cu and high Nb or Ti contents is most beneficial for a high pitting resistance of Zr-based bulk metallic glasses. The bulk glassy Zr57Cu15.4Al10Ni12.6Nb5 (Vit 106) and Zr52.5Cu17.9Al10Ni14.6Ti5 (Vit 105) alloys exhibit the highest pitting resistance.