How to remove Guest option from login screen?
@andyshinn
OK, 
I see on your screen shot, that is not Guest user icon, that is Group user!

It says Other (not Guest). 

The Guest user shows with one face, the group shows with multiple faces, like your icon.

I see you are at work. 
Do you have a group user account set up by your IT people?

Let me clarify that. 
Someone or something (a program) has put a login and hidden it from you so you can not delete it. 

Well you can now do something since you know about it.
First lets find out who! then decide if you want to delete it.