Can you get waves in water without gravity? Is it possible to produce water waves in absence of gravity?
 A: Waves inside a container are, in general, something to be avoided. Waves inside containers have capsized ships, derailed railroad cars, and rolled tanker trucks off the road. Waves and wave-like behavior of liquids in the fuel and oxidizer tanks in a spacecraft are also bad. Slosh has been a problem from day one in launching spacecraft, and continues to be an issue. The Near Earth Asteroid Rendezvous mission almost ended when slosh disturbances caused the spacecraft to go out of control. The second flight of the Falcon-1 failed due to unexpected slosh interactions. The partially successful SloshSat was launched in 2005 with the specific intent of studying slosh in zero g conditions.
The fluids (liquid+gas) in a partially filled tank that has been in free fall for a sufficiently long time are bizarre mix of gas bubbles, free-floating liquid blobs, foam, and liquid blobs and films crawling along the walls of the tank. This is a world of very low Bond, Weber, and Reynolds numbers. These dimensionless numbers capture the ratio of gravitational effects to capillary effects (Bond number), the ratio of inertial effects to capillary effects (Weber number), and the ratio of inertia effects to viscous effects (Reynolds number).
Firing a thruster results in forces analogous to gravity and cause the liquid to coalesce. The transient and wave-like phenomena that result can be very deleterious. Starting thrust should be very low (< 1/100 g) until the liquid coalesces. Stopping thruster firings can also result in transients. This short youtube video shows a camera inside one of the kerosene tanks on the Saturn 1. There is a very nice water hammer at about 1:35 into the video when the thrusters shut down.
A: For all oscillating systems there are certain forces that put them in motion and maintain them (gravity, shear, surface tension et cetera). When a stabilizing force like friction dominates the system the waves dampen gradually. That is the case in the video of a Nasa Experiment mentioned by @Anna Taurogenireva in the comment. It is possible and there is no reason why waves wouldn't be able to form when some of the usual forces are removed from the system.
