[Titanscape (OP)]

Is it possible to compress water to a smaller volume, under immense pressure such as that found at the core of Jupiter?

[MikeS]

Well it would certainly work in a neutron star or black hole, otherwise, probably not.

[imatfaal]

Mike - thats a bit off-topic, but

the whole jist of a neutron star is that matter is degenerate - water would no longer be water, hydrogen isn't even hydrogen; simplistically electrons are crushed into the proton in the nucleus to form neutrons.  in a black hole we simply have no idea of what matter will be like - there are presumptions that a further degeneracy happens but we really do not know

[imatfaal]

titan

yes you can compress water - but it is very difficult

A common statement is that water is an incompressible fluid. This is not strictly true, as indicated by its finite bulk modulus, but the amount of compression is very small. At the bottom of the Pacific Ocean at a depth of about 4000 meters, the pressure is about 4 x 107 N/m2. Even under this enormous pressure, the fractional volume compression is only about 1.8% and that for steel would be only about 0.025%. So it is fair to say that water is nearly incompressible. Reference: Halliday, Resnick, Walker, 5th Ed. Extended.

Quote from the excellent hyperphysics

[Soul Surfer]

The compressibility of water is around 40 parts per million per atmosphere of pressure.  This is around the same as many coomon metals expand or contract in 10 degrees centigrade temperature change so it is not insignificant.  If water was not compressible sea level would be significantly higher,  say around 10 metres from a quick guesstimate.  I have seen the figure elsewhere but can't remember it at the moment

[Titanscape (OP)]

So why is water so hard to compress? And is it the same with alcohol?

[Soul Surfer]

Ethyl alcohol is about twice as compressible as water.  A lot of other organic liquids are similar.  Mercury is much less compressible about one tenth of water.  Liquids are generally less compressible than gases because their molecules are held together by attractive forces at the temperature they are liquid so you are essentially trying to compress or distort atoms.  Gases generally have distinct spaces between the atoms and are more compressible and obey the ideal gas laws at low pressure. 

Very interesting things happen at the critical point of a liquid.  That is the temperature at which molecular energies prevent the molecules from holding together.  This is at about 30 degrees C for carbon dioxide  below that temperature it is possible to liquify carbon dioxide by pressure.  Above that temperature it will not form a liquid but may form a solid at a much higher pressure.  It is also interesting to note that liquid carbon dioxide is not stable at normal atmospheric pressure only solid carbon dioxide (dry ice).
The liquid state is a somewhat unusual state compared with solids and gases and depends on a balance between how well molecules stick together and how well they slide over each other.

Water is also rather special because it is essentially a polymer held together by its electrical polar nature because the molecule is asymmetric with a positive charge at one end and a negative one at the other.