Condensation on soft elastic surfaces differs significantly from condensation on hard surfaces. On polymeric substrates with varying cross-linking density, we investigate the nucleation and the growth of condensing water drops. With increasing softness of the substrates, we find (1) increasing nucleation density, (2) longer relaxation times for drop shape equilibration after merging of two drops, and (3) prevention of merging on very soft surfaces. These effects lead to higher surface coverage and overall condensed volume on soft surfaces.