In the WinXP days (I skipped Vista) it was the motherboard drivers which would prevent you from migrating your windows install between machines. In windows 7, that still seems to be the case but there are those who think you can hack out the manufacture specific drivers for generic ones and it will supposedly work. In my experience, this only works some of the time. There are a lot variables that have to line up in order to easily move a drive from one motherboard to another.
So to answer your questions:
- Yes, the windows OS cares when you move hardware architecture between Intel and AMD, but not generally because of the processors themselves. If you just hook up the drive to the new system, expect it to blue screen before loading into windows.
- No, you do not need to get another license. All non-OEM licenses can be migrated from system to system without breaking the EULA. OEM licenses can generally be migrated as well, but Microsoft frowns upon that practice.
So your "best" option is to backup your data, wipe the drive, and reinstall windows in the new system. This is guaranteed to work 99.9% of the time. (assuming you have good hardware)
Now if you are one of those people that have some "mission critical" software that for some reason can't be reinstalled (lost media, someone else installed, lazy user), there is a way to migrate your OS to new hardware. The bad news is that it takes a lot of work and is not recommended for "normal" users.
If you've worked in large IT departments, with hundreds of computers, you may have heard of something called sysprep. It's a OS deployment/replication tool that allows you to create something called an "image" that can be deployed to your organization. In this case, you would use sysprep to pack up your OS, removing machine specific information (SID,Drivers,HAL) and prepare it to do a partial reinstall on next boot. It's take too long to go over all of the details here, but I have links to others who have explained it.
Read the links, and if your eyes start to glaze over, do yourself a favor and just reinstall the OS. You'll be back up in a few hours instead of a few days. Trust me on this. Also, if windows activation gives you problems, Sascha's answer tells what you need to say. As long as you say that it's only on one system, they will almost always activate it.