0s and 1s

 But, why do you need an electrical signal? - I think the answer is that it is difficult to react to a nothing voltage (ie. involving lots of circuitry, with not gates etc), whereas if you have a voltage, you instantly know that the signal is a negative one.

0V is not a nothing voltage, it's just 0V difference from some reference point.  For example, if I have to 9V batteries and hook their '-' terminals together, I can measure 9V between the "-" terminals and either "+" terminal.  If however, I measure from one "+" terminal to the other, I get 0V.  Both are said to be a the same potential so there is 0V between them.  It's easy to detect and react to a 0V situation in an electronic circuit, in fact, this is quite common.

Maybe you could clarify the situation you are asking about a bit more.  There is a fundamental difference between a 0V signal on a conductor and a "nothing" voltage.  Basically, there is no concept of a "nothing" voltage as a voltage is always relative to some other point.  

BTW, when I said it's difficult to get a signal down to 0V, I meant that in the context of an electronic system having a 0V based power supply.  Something like +5V.  In this case, since the transistors used to pull the voltage down to the 0V power supply are imperfect, even under the best real-world circumstances, you don't ever get all the way to 0V.  If, however, we are operating using a split power supply (like +5V and -5V) then it's very easy to get 0V.  Now, of course, it's hard to get close to -5V.

  Yes, but what I originaly thought, (after being taught simple electronics in A-Level Physics), was that a 0 was 0v, and a 1 was Xv. The way this worked, was by having a circuit, with a switch ie, when the light is on, you get a 1, and when off, you have a 0. It seemed to me, therefore that it was unneeded to have voltage when giving a zero. But, I think, it is down to the handling of the message - If you ask a circuit something, and it returns a negative, with the original 0 = 0v, no answer will be recieved, unless you use etra circuitry ie. not gates etc, whereas with a 0 = .5v and a 1 = 5v, it is much simpler.

  Hang on - surely the way to get zero volts, is to create a short circuit?! - Wait!, - I know this sounds bad, but that is exactly how a Not gate works, so surely the same applies to a computer?

I think you're confusing 0V with a logic 0 and they are not necessarily the same thing.  The choice of which voltage in a digital electronic system is 0 and which is 1 is entirely arbitrary and chosen for the convenience of implementation.  For example, an older logic family used in many supercomputers is called ECL.  It used a -5.2V power supply and had a logic 1 at 0V and a logic 0 at -5V.  There is no special relationship between 0V and logic 0 in a digital system.

 Well, that was what the basic question was - why the logic 0 had to be represented by something other than 0v? Which as you say is because of the implementation.

Right, it's really up to the designer of the technology to choose what is a logical 0 and 1.  In what is commonly called "standard logic" because of it's widespread use, a logic 0 is around 0V and a logic one is higher than 2.0V.  Again, however, it's entirely arbitrary.