Toothpaste and water
Drops or patches of water in your sink are basically water that is not evenly spread out. The surface tension of the outermost water molecules acts a bit like a "balloon" containing the inner molecules. To a small degree it is thus possible for the water molecules to be stacked on top of each other because the water's surface tension is stronger than the gravitational pull. 

Toothpaste contains detergents like sodium dodecyl sulfate which act as a surfactant reducing the surface tension of water. 
When you coat your finger in a mixture of water and a weak detergent like toothpaste or a stronger one like soap and touch the water drops in the sinks, the water mixes with the detergent. This lowers the surface tension and gravity spreads the drop out. The water is thus not really moving away from your finger, but the drops are being spread out under and around your finger.