Does water turn solid under deep ocean because of high pressure? I know that we can make water solid with high pressure, so I think water will be solid in the deep ocean?
If that is true, the depth of the ocean would be limited because water will become ice? Anyone know that maximum depth? 
 A: You are mistaken. Actually, you can melt ice by applying pressure. This is why ice is so slippery; when you step on a frozen lake, you are melting the very first layer of water, and thus creating a very good instant lubricant for you to slide on. It is a common knowledge false fact, see comments. 
Ok, granted, at very high pressures water does become solid. From the phase diagram, to get solid at around 0 °C you need around 650 MPa. How much is that? Pressure depends with depth as:
$$P = \rho g h$$
Assuming constant density, you need a column of water of $66\ \mathrm{km}$ for ice to be formed. That is about six times the depth of Challenger Deep, in Mariana trench.
So the answer is no – on Earth. You will not find enormous amounts of more or less pure liquid water anywhere else in the Solar System, but if you are happy with hydrogen, helium, and other gases, you may find it around Jupiter's core. Definitely, liquid H and He.
When water is mixed with other elements, the phase diagram is perturbed. For example, salt in the sea at atmospheric pressure lowers the freezing point about a couple of degrees (depending on the concentration). If water is mixed with hydrogen, helium, methane, and company as in a gas giant, the diagram will be drastically changed, so more detailed computations would be needed. 
