Officially, the OEM version needs to be tied to a single PC and cannot be transfered to another. Usually that is the motherboard, since that contains most of the devices. Adding a SSD (and thus moving/reinstalling Windows to it) is same as changing HDD, or simply reinstalling.
So you can reinstall windows to the new SSD (easiest solution) or move the current installation to the ssd (harder). The latter needs cloning software and some minor tweaks good for SSDs (these are done in the former case if Windows detects an SSD installation target).
Usually an OEM key will activate online ok, unless the new installation is very different (I really don't know how much difference counts) and you already activated in the past 6 months (at least that was an unofficial rumor for XP). In either case, you can activate by call.
As mathew said. If you later move to a different setup (e.g. motherboard, or newly built pc) you'll need a different key. Microsoft allows a limited number of such transfers (and you'll need to plead your case with MS for any key change required)
Of course, you can only run 1 windows copy in 1 pc (for the same key) - can't install in multiple pc's.
That would happen if you installed the ssd and reinstalled Windows. But if you clone the existing drive and transfer the OS to the ssd I think that it wont be an issue because you wouldn't be installing from scratch!
I cannot stress this enough. DO NOT clone a harddrive to an SSD as the above post says. windows will not be setup right and may cause problems with your SSD.
An OEM version of windows is tied to the motherboard. You can reinstall it as much as you want. You bought it. it's you're OS. The licensing agreement says its for that PC/board. The WORST that will happen is it may not automatically activate if you've reinstalled it a dozen times and you may have to call Microsoft to activate it.