I had one cd (driver's license theory exercises) requiring a key based on your hardware configuration and it was a never ending nightmare.
Problem 1: I use up to four different computers (being: my own (at home and at my parent's house), my parent's computer and my boyfriend (well I guess I should be saying my fiancé now <img src="/ubbthreads/images/graemlins/smile.gif" alt="" /> )'s computer.
If I remember correctly, the combination you had to enter was based on your cd key AND on the hardware config. (Using the cd key to make sure one cd only gets one key). So, for starters I had to request for different keys.
You got the first one for free, but starting with the second one you had to call/send an email to the support requesting another key, explaining the reasons why you needed another key.
So far, so good.
Problem 2: I have two different sound amplifiers (a little one and a better one for when playing opera music etc. from the computer). Alternating these two gave a different hardware config, and thus a different cd code.
Also, back then I had only one port which could be used for either the printer or the scanner. Again, alternating the two gave a different hardware config.
It's a good thing I never needed those driver license exercises for a long time, because even in the few weeks I actually needed them they gave me a real headache.
And oh yeah, by the time my brother and sister were learning the theory, we had bought a new computer and we had the same problems all over again...