I am worried about allowing more than one user of my WordPress installation use WordPress at the same time.
What if one user updates a page or deletes a page while the other user is editing it? How robust is WordPress under this multi-user case? I am talking about users who are logged into WordPress as editors.
If two users attempt to modify a page, does WordPress still work correctly?
As far as writing/editing pages and posts WordPress is pretty darn good at handling multiple users and conflicts. There are clear warnings and error messages to the user that someone else is actively editing the post/page. And it will prevent you from saving changes if another user opened the post/page before you did.
Also, when a user opens a document for editing you can take over editing. This helps when for example the user runs out to lunch or home for the day, the document is not blocked for editing.
To see it in action simply attempt to edit a post/page from two different user accounts and browsers.
Note: Edits reflect improvements in WordPress since the original answer was posted.