What is it called when water sticks to other things?

Water molecules form weak hydrogen bonds with each other when close, which causes them to stick together. This is called cohesion. It is one of three highly unique properties of water, the other two being adhesion, which is water's ability to stick to other materials, and surface tension, which causes the water molecules to act almost like an elastic sheet, like when water is on the lip of a glass, but doesn't spill.