Aside from carbon, what materials change structure under intense pressure? I was thinking the other day about what sort of exotic materials one would find in the depths of a planet. I have heard theories about how an enormous diamond might be found in the centre of gas giants.
Current theories have a ball of iron at Earth's core - would that be like the iron up here on the surface or does the pressure change its structure?
So here's the question: Aside from a carbon becoming diamond, what materials change structure under intense pressure? 
 A: Water has a very complicated phase diagram with several high pressure states.
A: A pretty recent example is given by the perovskite-to-"post perovskite" structural change of magnesium silicate at sufficiently high temperature and pressure. It doesn't seem particularly exotic, but perovskite materials are exceptionally stable and ubiquitous, and discovering a new high-pressure phase was a major coup for deep earth geophysics.
A: 
theories about how an enormous diamond
  might be found in the centre of gas
  giants.

Hmmm, because Diamond is still somewhat away from 
a closest package, the giant planets may contain a 
sort of carbon denser than diamond, metallic 
in properties. 
In general, all substances (not only crystalline) 
will transform into something with a densest package 
of atomic cores and a delocalized electron gas: 
metals, if only pressure is high enough. 
For hydrogen, some experimental research was/is 
done to find this "metallic" form. I remember an article 
in SCIAM some years ago. 
Of course all this is valid only if temperature is low enough. 
(For that reason we speak of planets cores!)
But at the end of pressure scales in neutron stars all materia 
transforms to neutrons irrespective of enormous temperatures,

would that be like the iron up here on
  the surface or does the pressure
  change its structure?

One difference to "surface iron" is obvious: the innermost core is solid, in spite 
of the temperature. And one has to be aware that the iron in the core is not 
pure, there will be some other metals and carbon in the melt of outer core. 
At the border of outer core and mantle sometimes sulfides are assumed. 
A: This is a common feature of many (if not most) crystalline materials. Iron in the inner core of Earth presumably has $\epsilon$ structure. To see the difference between $\alpha$ and $\epsilon$ structures of iron, see pictures at the bottom of this webpage.
A: Lots of materials change under pressure. Many of the products you use everyday wouldn't exist without high pressure processes. Practically any material has a denser form when subjected to high intensity pressure. It's also likely to change the chemical bonding in the process of applying the high pressure as bond energy is inter-reliant on pressure and temperature. Increasing the internal pressure and seeing the results of this would be a good experiment to carry out on a material, as temperature is constant (ideally) when pressure increases. 
The best results are when you combine temperature and pressure to create denser materials. Sintering (not pressure-less sintering mind you) is a great example of this, although generally if you do it with metals you'll want to do it in an inert gaseous atmosphere. Lots of nuclear materials rely on sintering, ytteria oxide powder is a good example. 
Iron at the core, depending on whether it has impurities and is at a given phase will certainly be denser at the core. I'm going to assume given the nature of solid solutions and other minerals down there that it'll probably be quite dense.    
