Yes. Many gases, including oxygen, dissolve in water — though oxygen dissolves only to a small extent.
Small as that amount is, everything living in a pond, a river or the sea depends on it. Fishes, aquatic plants and other water organisms take their oxygen from the water itself, not from the air above it, and it is this dissolved oxygen that keeps them alive.
Why it happens: Gas particles at the surface of the water are constantly striking it, and some of them slip in between the water particles and are held there. Because gas particles are already far apart and are not tightly bound to one another, they need no tearing apart the way a salt crystal does — but water can hold only a small number of them, so the solubility of a gas is low.
Did you know? The fizz in a cold drink is carbon dioxide dissolved in water under pressure. Open the bottle, the pressure drops, and the gas comes out of solution as bubbles.