Under "Sharing" in System Preferences, I do not have anything shared. However, I have a "Shared" folder under "Users". Is there a way to remove this folder?
Yes, it's possible, but that doesn't mean you should do it.
Finder/etc doesn't stop you deleting it, and it's not a 'system' directory (despite being created by the system), but is it causing a problem, enough that you want to delete it? Apps can depend on that directory and deleting it could cause problems, now or in the future. I don't have any examples of such applications, but that's not to say they don't exist or may exist in the future.
You should follow what George said, it's not going to cause any problems by just being there.
However, if it's bothering you simply being there then hide the folder using
It will still exist, applications can still use it, and you won't see it anymore.