This is called adhesion. Water is very very sticky and it likes to be attracted to things. It is far more attracted to the side of the glass than the air. Gravity has some effect, but not enough until theirs is more liquors with more mass.
Water also has a property called cohesion, where it sticks to itself. This is why there is a water droplet in the first place. The molecules of water stick to each other, and therefore they go down the side of the glass to stay with the molecules that are attracted to it.
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