I'm interested in investing in power functions based trains, but want to automate switching points. Is this possible? What is the cheapest / easiest way of achieving this?
There is a pure way of changing the points at a track. It requires as few pieces as you like: a motor and two technic beam/bricks. This video demonstrates the principles of point changing with a NXT motor and will work with PF and RCX.
You can use Mindstorms to program the events that trigger the points to change, it will cost you extra but there are benefits.
One elegant solution is to use pneumatic elements, as a small pneumatic pump is enough to move the lever. If you're lazy to figure out how, you can buy a kit from a fan which will allow you to control 2 points (you'll need one more pump to generate the pressure). With the included instructions, you can build more controls if you have the parts, or simply buy more kits. (He also sells compatible pneumatic hose by the meter, and his custom waggons are nice as well).
His design is very compact, probably much more than you'll be able to get with electrical power; plus, it saves energy. The only drawback in my opinion is the hoses which you'll need to run from your control station to each point, which are slightly larger that electrical cables.
Another typical solution is to use a motor which controls the point. This will take more place, and you have to be careful that the motor doesn't run too far (use a clutch gear). One promising way is to use the new small linear actuator: which should behave more or less like the mini pneumatic pump; but of course any other Technical solution should be good. Use your imagination, or dive into BrickShelf in search of inspiration.
Of course, you'll need to run electrical wires, or use infrared receivers, but then you'll be limited in the number of points you can control. Note that sometimes, the configuration of your layout means that pairs of switches can be controlled together (think of a bypass to change from one track to the other), so that you can spare some control channels, or wires.
Non-LEGO solutions can be achieved with about anything, including solenoids (electrical actuators), which LEGO doesn't produce. One other elegant solution I can think of is to use bike brake cable, but I have no real idea if that would be easy to do.