Being in a large corporation, I can recall many examples for this. But mostly what it will come down to are the tools you use, and how effectively you can use them.
The group I work in, we have around 6 people. We administrate thousands of desktops[neighborhood of 3500-4000] (WinXP/RHEL5) as well as a few hundred servers[700-ish total](AIX,HPUX,Solaris,Linux,Win2k,Win2k3). (about 720 machines per admin) We are able to do this because we have defined and refined our rules on how issues are handled, as well as tweaked the tools we use to administrate. We have scripted pretty much any reoccurring action we have, one rule being that if it had to be done more than two times in a month, it needed to be scripted and automated. Most menial tasks such as user account creation, kickstart/jumpstart/ghost/etc, software installs, service configuration, are for the most part - handled by clicking a button on a web page. Unless something is physically broken and parts need to be ordered, we can normally get machines going again within 30 or so minutes if we were not all busy reading fark, slashdot, or facebook.
The other 'large' group that we know about, they manage about 1100 servers. all production. they have about 45-50 people. (20-ish machines to 1 human). For the most part, they do ALL administration by hand. Need to update the hosts file? Log into every machine, obtain rootly privledges, edit [/etc/hosts or C:\windows\system\drivers\etc\hosts] by hand using your favorite text editor, save, close, logout, and repeat. Their only saving grace is that they have very very very strict standards on what is allowed to be used on those machines, both hardware and software. If a part breaks, they already have spares on hand. A compiled needs to be installed? you have your choice of 2 compilers, and each choice has 3 versions you are allowed to choose from. And there is no "Other _________" option. Ever.
Yes, it's true that each system administrator will have their own silly custom scripts that do some small activities, like creating a home directory or installing a piece of software. But as a group, would it not be better for everyone to have access to these tools so the whole group can perform at a greater efficiency?
Also, users are stupid. Especially the dumb ones. Set up a ticketing system for trouble tickets and post updates to that as you work on the problems. Users will tend to leave you alone more as they think you are working exclusively on their issue with all the pretty updates.
Also, fyi. Upper management liked our tools so much that they are telling the other 'large' group that they need to start using them as well.
