If water stopped flowing (it would stop flowing downwards from mountains and all) then, would it start rising upwards? If it floats on the space ( I say space because there'd not be any atmosphere) above the sea level, would droplets of it be floating here and there or would the whole mass of the water body (say an ocean) be floating? Will they dry up eventually?
The most important effect will be the fact that the earth is rotating. At the equator the earth is moving approximately 1000 MPH (somewhere around 1600 kph). Water, and everything that isn't nailed down, would tend to keep moving in a straight line. Due to the earth curving downwards, it will look like everything begins floating... and accelerating upwards. It would be approximately a half inch (1 cm) in the first second, and about 185 feet (56 m) in the first minute.
There is a second noteworthy effect with the atmosphere. The atmosphere is a gas under pressure (14 pounds per square inch at sea level, 700 kg per square meter), confined by the force of gravity. If gravity vanished it would experience the same effect described in the previous paragraph, however it will also attempt to expand. At ground level the atmosphere will start losing pressure, but it will remain in place for a while due to pressure from expanding gas at higher altitude.
The oceans might "stick" to the seafloor for a second or three, but they will quickly peel away leaving a near-vacuum underneath. The surface and edges of the ocean will rapidly become chaotic and break up, as the remaining air pressure tries to drive-through to fill the vacuum underneath.
Somewhere on the scale of 30 minutes to an hour air pressure will diminish to negligible levels, all water and all free-objects will be miles above the earth and rapidly flying away. The oceans and other bodies of water will be a chaotically expanding froth, simultaneously boiling and freezing. (At zero air pressure, the boiling point of water is approximately 32F / 0C.)
If gravity from the sun also ceases to exist, everything will quickly fly out of the solar system. The water will become random-sized comet-like ice scattered into interstellar space.
If the gravity from the sun continues to exist, the water will form a ring of ice-chunks around the sun similar to an extremely sparse version of the ice rings around Saturn. However that ice will not remain stable long-term at that distance from the sun. The sun will prevent it from reaching the most extreme deep freeze. Over many many years, the ice will sublimate into gas. It will be pushed out to the more distant solar system where much of it will re-crystallize as microscopic dust. It will slowly be swept up by more distant planets, join the ice of comets and other outer debris of the solar system, be swept out of the solar system entirely, or it will be split by radiation into hydrogen and oxygen.