On all the Linux systems I've managed, the root account has a GID and UID of 0. Is this guaranteed, or is it possible that the system will give root a different ID?
There are actually two parts to your question.
Yes. As is pointed out by Rich Homolka in a comment, there's code in the kernel which explicitly checks for uid 0 when needing to check for the root user, which means that root always has at least uid 0.
It's also worth noting that, as pointed out by Simon Richter, on BSDs there often exists a second uid 0 account, by convention named
1) the administrator is always uid == 0. This is coded in the kernel. It would take some coding in the kernel to change this. There's not much point to this, so it's not done. For example, it would be inconsistent for other unixes sharing the same NFS for example.
2) uid 0 does not necessarily map to root. The best example is FreeBSD. It has two uid == 0 accounts, the difference being the shell. root has shell /bin/sh, which is a simple shell, useful for when your disks are bad and you need fsck /usr. toor uses tcsh, which is much more useful in non-emergency situations,since it has things like history, etc.
Another, more personal example; one job I had where they had a root equiv (i.e. uid=0) account over NIS. The password, blank! Because the new sysadmin couldn't remember the root password on the machines. I yelled about this for obvious reasons (NIS passwords by definition can not hide their blankness). I was not happy about this account.
And it really isn't the system that gives uid 0 is root, it's you. You change this my using passwd files, or other naming directories (NIS, ldap) but it's not compiled in. Though you should have at least one uid 0 account in /etc/passwd, since you may not have networking when you really need it.
So root is always uid 0, but uid 0 is not necessarily always root.