Attached to each licence (upon activation) is a complete list of Hardware IDs. Basically they know what your computer looks like (at least, the parts that make it up, like the CPU, RAM, MoBo, etc). They won't care at all if you change one or two things (say, switch CPU, or switch RAM), but they will care when they detect an entirely different system running an already used licence. That's when you get the warning that you may be the victim of counterfeit software and you should activate it with "genuine" windows. I.e. you have to call them up - the process is quick and straightforward.
So basically, the only way you can use the same key on multiple computers is if you don't activate windows (namely, don't go online and get the various windows updates).
You can crack your other computers or use fake serials, but that's illegal (not that anyone can stop you). You can fork a bit out and get the Family pack for multiple licences, but it's only slightly cheaper than just getting it off Amazon. You can just go and buy a licence for each comp, but that's expensive (at least, I think it is).
An extra option is find someone who is a student at University. Students taking IT-related courses can get Win7 for free from their course advisor/convener. Anyone else has to fork out £30 for it (and more if they want a permanent download link and/or a DVD backup). If I recall, it's limited to one copy per person, and is done entirely through the student email account.
What you do is up to you.
