Air is an example of a fluid that exhibits this behavior. For a test of this, close off the end of a bicycle pump and notice that the volume gets smaller as the pressure increases. Because of this property, the density of air is not a constant as one ascends into the atmosphere. This is why you have so much trouble breathing at high altitudes. However, not all fluids are as compressible as air.
Water is almost totally incompressible.
Therefore, as one goes deeper into water, the density of the water almost stays the same. A demonstration showing the difference between the compressibilities between air and water is the Cartesian Diver. Fill the soda bottle almost to the top with water. Place the eyedropper in the bottle with the rubber bulb up. The eyedropper should float in the water.