Is it possible to build a site without Users and Node?
With Drupal 7 and a reasonable amount of effort, I don't actually believe it's possible.

Drupal 8 however will further decouple the modules, so that you can (hopefully) truly build a site without it.

A good use case for disabling User, is as a security hardening mechanism. Have your production site completely disallow logging in by not having the module, and push content from an internal stage environment instead with the help of something like Deploy.

A good use case for disabling Node could be a file handling API. One would need the file entity, but then only communicate with the world through a REST based API. No nodes (or even theme) needed.