What would happen if I take a glass of water in space? What would happen if I take a glass of water in space i.e. outside the gravitational influence of earth?
My teacher said that the water would vaporize but I am not completely satisfied by the answer.
I feel that it will still be in the glass because of adhesion forces.
Am I correct?
 A: Your question is a little ambiguous. When we refer to "space", it usually implies "vacuum". In your question, however, it seems like you're simply referring to a zero-g environment (e.g. an orbiting spaceship).
In a vacuum, the water would boil away. So, "vaporize" is pretty much correct.  The boiling point of water drops with decreasing pressure. Since there's zero pressure in the vacuum of space, there's nothing "stopping" the water from boiling away. (This effect is independent of gravitational influence (on Earth scales, anyway))
If by "space" you mean "aboard a spaceship with a pressurized cabin and zero acceleration", then the water would indeed stay in the glass, but it would be quite unstable, since the slightest disturbance of the glass would cause the water to spill out.
A: I don't show any contradiction regarding Brant's answer. But, There's a difference between evaporation and boiling. Evaporation is a surface phenomena where molecules gain energy through random collisions. But, Boiling takes place throughout the entire volume where the molecules change phase throughout the volume of liquid.
Ok.. Now back to the question: There are two things to put our eyes into...
Boiling point of water is $100^oC$ only at normal temperature (298 K) and pressure (1 atm). As altitude increases, pressure decreases and eventually attains a near-zero kPa in space. This decreases the boiling point of the liquid (water) according to $PV=nRT$. Hence in space (vacuum), water definitely boils..! (But, mentioning "outside the gravitational influence" is non-correlated here...)
Now, Triple point of water comes into play. Wiki clearly says that - At zero pressure (which is below the Triple point), it's impossible for water to remain as liquid. Hence the left-over form - "GAS".

At pressures below the triple point (as in outer space), solid ice when heated at constant pressure, is converted directly into water vapor in a process called sublimation.

Temperature in outer space could be 2-3 K. Once a good amount of water has boiled from the liquid phase, there would be an isolated area of water molecules which are at the coldest place of their lifetime. They would suddenly freeze and form ice crystals (similar to a desublimation). See this paper for a brief conversation on the topic... Astronauts have proved this in space.

When astronauts urinate in space and release the contents, the urine rapidly boils into vapor, which immediately desublimates or crystallizes directly from the gas to solid phase into tiny urine crystals. Urine isn't completely water, but you'd expect the same process to occur with a glass of water as with astronaut waste.

But, it could be achieved simply by using a home-experiment producing snow by desublimation.
Note: This kind of rapid boiling & freezing would overcome the adhesive forces drastically under such conditions... So, no sticking to glass.
