Man, all you guys and your "scientific" explanations make me laugh...
I would like to start by saying I don't suggest cutting springs to anyone, but IF done correctly, the only adverse effect will be the greater potential of hitting the bump stops.
Now, if I have a spring, doesn't have to be an automotive spring, and cut it in half, does it's spring coefficient change? If it is a linear spring, then no, it does not. I have not altered any of the material properties of the spring in any way (heat treating however, does have an impact and I highly suggest against doing this). Now with progressive springs it's a little different. Progessive springrates mean that as the spring compresses the coefficient (and therefore transferred force) increases. Instead of the force being a direct correlation (F=kx), the spring coefficient, k is now a function of x (F=k(x)*x). So in this case, cutting the spring will cause the rate to change. Cut off too much and the ride becomes bouncy. Cut off just a little and it will only be a little stiffer than stock. It's all about moderation. Too many people are are used to seeing guys cut off WAY too much and killing functionality. Truth be told, if done accurately and carefully, cutting the stock springs will result in a similar springrate and ride height as some of the progressive springrated aftermarket springs out there. I'm not saying you get the same quality, but the end result will be similar, especially with aftermarket shocks.