We prove that CdS nanocrystals can be thermodynamically stabilized in both wurtzite and zinc-blende crystallographic phases at will, just by the proper choice of the capping ligand. As a striking demonstration of this, the largest CdS nanocrystals (similar to 15 nm diameter) ever formed with the zinc-blende structure have been synthesized at a high reaction temperature of 310 degrees C, in contrast to previous reports suggesting the formation of zinc-blende CdS only in the small size limit (< 4.5 nm) or at a lower reaction temperature (<= 240 degrees C). Theoretical analysis establishes that the binding energy of trioctylphosphine molecules on the (001) surface of zinc-blende CdS is significantly larger than that for any of the wurtzite planes. Consequently, trioctylphosphine as a capping agent stabilizes the zinc-blende phase via influencing the surface energy that plays an important role in the overall energetics of a nanocrystal. Besides achieving giant zinc-blende CdS nanocrystals, this new understanding allows us to prepare CdSe and CdSe/CdS core/shell nanocrystals in the zinc-blende structure.