Water VS Soapy Water I recently did an experiment.
I have a cup of tap water, and a cup of tap water mixed with soap.
I used an eyedropper to slowly drip drops of tap water onto a penny.
Then I cleaned the penny, and dripped soapy water onto the same side of the penny.
My results are:
Tap water: 32 drops
Soapy water: 20 drops
Can someone tell me why that is?
Did the soap in the soapy water break the surface tension?
What happened?
 A: When you put a drop of liquid on a solid surface the surface of the liquid will meet the solid at a characteristic angle called the contact angle.

The contact angle is measured through the liquid so a high contact angle means the drop tends to ball up while a low contact angle means it tends to spread out. I've labelled the contact angle as $\theta$. I don't know what the contact angle of water ona  coin is, but I'm guessing it's quite high so the drop would look a bit like the drawing on the left.
When you add a surfactant this usually lowers the contact angle, so the drop will look more like the drawing on the right.
Now suppose you keep adding water until the drop covers the whole coin. The result will be a magnified version of the diagram above:

I've kept the contact angles the same as they were in the first diagram, and it should be immediately obvious that the lower contact angle diagram on the right doesn't contain as much water as on the left. That's why you were able to add more drops of pure water than of soapy water.
In practice the difference wouldn't be as big as my diagram suggests because the weight of the drop will deform it. So the pure water drop shown on the left would squish down a bit and this will reduce its volume. However even taking this into account the higher contact angle drop will contain more water than the lower contact angle drop.
A: Surface tension is the answer. Soap contains surfactant whose purpose is to lower the tension. So, it wets the penny better rather than balling up, and the size ball that can be held together is smaller.
I did some testing on the behavior of single water drops, and here is a photo from that page:


This is a photograph of some ordinary water drops, along with some drops that have had a little bit of Triton X-100 added. You can clearly see the water drops as little lenses that are standing quite tall off the plastic, and have pronounced optical effects due to their strongly curved shape. Meanwhile, the other drops are clearly more wet, spreading out over the plastic into a thin layer. They are irregularly shaped as it has less tendency to pull itself into a ball, and will spread out very flat. I’ve added arrows to point out the bright highlights at the curved edges of the drops because they are so hard to see.

