What would happen to matter if it was squeezed indefinitely? I hope that this is a fun question for you physicists to answer.
Say you had a perfect piston - its infinitely strong, infinitely dense, has infinite compression ... you get the idea.  Then you fill it with some type of matter, like water or dirt or something.  What would happen to the matter as you compressed it indefinitely?
Edit:
I'm getting some responses that it would form a black hole.  For this question I was looking for something a little deeper, if you don't mind.  Like if water kept getting compressed would it eventually turn into a solid, then some sort of energy fireball cloud?  I'm not as concerned about the end result, black hole, as I am in the sequence.
 A: I'll convert my comment into an answer, because I think it answers the question:

A black hole would form, because eventually you'd surpass the matter's Schwarzschild radius.

The Schwarzschild radius of an object of mass $M$ is
$$R=\frac{2GM}{c^2}$$
Compress any amount of mass into a sphere with a radius smaller than that and a black hole will form. Now, for small amounts of mass like this, it will most likely evaporate very quickly via Hawking radiation, but a black hole will form nonetheless.
Any amount of mass can form a black hole if strong enough forces are acting on it. Here, the force is not gravity - at least, not the force causing it to undergo the collapse - but the force applied by the piston.

Regarding the edit - If you compress liquid water enough, then it most likely will not turn solid. You can see this by looking at a phase diagram, which shows how the state of a compound changes with temperature and pressure. Here's an example of a generic phase diagram:

Now check out water's phase diagram here. Water has a chance at becoming solid only in a very narrow range of temperature and pressure, if it starts off as a liquid.
A: You asked for process. I'm assuming infinite material strength here, as in the piston cannot be stopped (infinite force on an infinite strength material that can resist infinite temperature).


*

*Solids will be compressed, resulting in lots of heat as this happens (with infinite pressure, and infinitely strong materials and thus force, the matter will give), until they reach a liquid state, gaseous state, or start losing electrons and ionizing, or just stays solid all the way up to Electron Degeneracy - it depends greatly on the substance what happens here. With current realistic materials, the piston would break. Since it doesn't break, and there's infinite force behind it, the substance gets compressed and heated anyway.

*Liquids will be compressed, resulting in lots of heat as this happens (with infinite pressure, and infinitely strong materials and force, the matter will give) into a gas, plasma, or Electron Degeneracy (depends on substance). With current realistic materials, the piston would break. Since it doesn't break, and there's infinite force behind it, the substance gets compressed and heated anyway.

*Gaseous substances will then easily compress, resulting in lots of heating as they do, until they heat up enough that the electrons freely float among the nuclei, and you have just made a Plasma.

*Now at a Plasma, the matter is slightly ionized (+1,+2) as the outermost electrons will have escaped and thus resulting in positive charges. The matter will continue to compress and heat

*More compression, resulting in more heat. More electrons are too energetic to orbit the nuclei, resulting in higher positive charges (+3,+4 as allowable...).

*More compression, resulting in more heat. More electrons are too energetic to orbit the nuclei, resulting in higher positive charges (+5,+6 as allowable...).

*More compression, resulting in more heat. More electrons are too energetic to orbit the nuclei, resulting in higher positive charges (+7,+8 as allowable... until they're all gone). At some point you will surpass electron degeneracy pressure and form:

*Electron Degenerate matter where no electron can orbit the nuclei, but now freely traverse the highly positively charged nuclei 'soup'. Keep adding pressure, and you'll form:

*Proton Degenerate matter where only the repulsion of the protons is holding the nuclei apart. Keep adding pressure, and you'll form:

*Neutron Degenerate matter where the electrons and protons join and cancel, leaving you with basically a huge neutral atom full of mostly neutrons, being held apart by the quarks. Keep adding pressure, and you'll (in theory) form:

*Quark Degenerate matter where the quarks, or at least the standard up/down quarks, can no longer hold the pressure and perhaps combine/change form. Keep adding pressure, and in theory you might form:

*Preon Degenerate matter which would sort of be like one big subatomic particle (though you might skip this one), and finally:

*A singularity aka Black Hole
A: 
Then you fill it with some type of matter,

Why do You want to do that? Your piston is ", infinitely dense, " 
so You are going to compress matter with a black hole piston :=)
A: Presumably, it's going to be similar to the Big Bang in reverse, which is also what happens at the singularity of a black hole or any situation where matter is continuously compressed.
(Beyond a certain point, we don't really know.)
