What would be the state of water in interstellar space or vaccum?
tl;dr: ice

Let's have a look at the phase diagram of water:



In space, both the temperature and pressure are very low. That would put beyond the bottom left corner of the diagram, well within the ice field. So simply speaking, water would be ice.

However, there is the concept of vapour pressure. Any condensed material (just a fancy word for both solids and liquids) has that same material in the vapour around it. That's why you can smell alcohol, even though it's liquid as one example. That's why a puddle of water will eventually dry out even though it's below the boiling point of water.

The way vapour pressure works is that if you look on the phase diagram, for a certain temperature, the liquid-vapour and the solid-vapour lines have certain pressures associated with them. For example, if you look on 50 C, then the pressure on the curve is 10 kPa. Roughly speaking, this means that in atmospheric pressure, one tenth of the air (which is at 100 kPa) has to be water vapour. If it's any less, water will keep evaporating until it reaches that amount. On Earth, wind and diffusion will disperse the water so it will basically evaporate until there are no more liquid water left.

Now let's think what would happen in space. The temperature is very low, so the vapour pressure is very low. Thus, it should evaporate also in space. However, because the vapour pressures at such low temperatures are extremely low, you might end up with a situation where the gravitation of that ice blob is enough to overcome evaporation, so that will be an agonizingly slow process.