The essence of a logo, the only reason to have one, is that it builds recognition by repetition. Any variation, then, reduces its effectiveness by delaying the point where it achieves "instant recognition."
Scott's example is a good one. The base FedEx logo, with its "subliminal" arrow, was in use for many years before they began to alter one element to identity related but different "sub-brands." It is a very distinct and recognizable graphic form, and that form doesn't change at all. FedEx succeeded where, to take a recent example, Pepsi bombed.
There are only two major things that make a logo: its form, the major element, and its color. Neither should change. If the form must adapt for different purposes, you can get away with it if you carefully rearrange elements without changing their forms, but it's risky, and in that case you mustn't alter the color.
If the form is strong and distinctive, you can risk color variations as in the FedEx example, but then you mustn't change the form.