Repeat the experiment. Gravity flattens the droplets, cohesion holds the droplets together, and adhesion keeps the drops from rolling off the coin. The cohesive forces, or the pull of like molecules toward one another, ensures that each successive drop will join the others. Cohesive forces create water surface tension, which is the tendency for the water's surface to withstand a push or a pull. That's why water looks like it's wrapped in an invisible skin.
Soap reduces the cohesive force, and breaks the surface tension.
Soapy water makes smaller drops than plain water. Since soapy drops are smaller, more soapy drops will fit on a penny than plain water drops.