Fighting piracy is a matter of trying to eliminate the masses from being able to easily use a pirated copy of the software... there's no full-proof method to both keep pirated copies unusable and keep your users sane when trying to use the software that they legitimately paid for.
As mentioned above, Windows monitors the serial numbers of certain system components, and if enough change, it triggers Windows to revalidate. Replacing a single component usually won't do it (graphics card, processor). Even if it triggers, you should just be able to activate over the internet unless it's been attempted too many times, in which case you may need to call Microsoft.
Calling Microsoft isn't a bad thing though (assuming you actually have a license and you're not reading it off a text document you found on the internet). It's a matter of understanding the terms of the license... if you tell them you're trying to install Vista (or XP) on another system, then no, you won't get a validation code. On the other hand, if you've had most of your system components replaced due to physical damage or just because you wanted to upgrade your motherboard, CPU and graphics card all at the same time... as long as you're still using it on one machine they shouldn't have a problem activating it. Trying to get the same product key activated many times over a short period is sure to send up red flags though.
I don't support (well, encourage) piracy... I'm just saying if you have a license key sticker sitting in front of you, and it's not a key you found on a search engine or generated by a key-gen, then you shouldn't be worried about needing to make a 2 minute phone call to Microsoft to activate the license you've already paid for anyway.
...all this said referring to home use though. When it comes to business use, it's best to have a license for every machine... it's just not worth the fines. All it takes is a disgruntled employee visiting http://www.siia.net
and filing a report to get audited, and the fines for piracy definitely aren't worth the risk. But that's a little off-topic...