It's very difficult to precisely control output at the rails. With bipolar transistor outputs, for example, you can only really get to within a diode drop of either rail. Op-amps in particular are often used in applications where you want accurate output either down to and including 0V, or right through to some negative value as well (think audio or some sensor applications). In order to achieve this you need to have the power supply a little bigger than the range of voltage you want on the output or you run into distortion problems where the output SHOULD be x but you can only get to x+0.7V or something, where x is usually 0V or the positive supply voltage.
There is also a similar problem where your design might end up saturating the output of the op-amp. This means that your input has caused the op-amp's output to slam into one of the supply rails. This does not harm the op-amp in any way, but it usually takes the op-amp a lot longer to recover and this also leads to distortion. By giving the op-amp a power supply that is larger than the output swing you want you can help avoid this (and you can help prevent it in the first place with clamping or limiting circuits on the inputs).
Also if you think about it, if your circuit is designed such that you want your op-amp output to be able to swing both positive and negative, the op-amp needs a power source that can provide this.
There are such things as rail-to-rail op-amps which use various tricks in order to get (within millivolts) of the rails, but you usually pay for that with increased distortion.