Legally, Microsoft defines your motherboard as your computer. If you change the mobo, then it counts as an OS installation on a second computer. With OEM Windows, the OS will throw a fit. If you have Retail Windows, you can install up to five times, so unless you've already installed that same copy of Windows five times you'll be ok. Now, if you change your mobo because it failed and you had to get a new one, just call up Microsoft and they'll give you a code to re-activate Windows.
If you make significant hardware changes to your computer, such as upgrading the hard disk and memory at the same time you'll need to reactivate Windows. If a major hardware change requires activating Windows again, you will be notified and will have three days to activate your copy of Windows. You may need to call Microsoft in order to verify that you're not installing a single copy of Windows on multiple computers.