Why does Gnome 3 not display files on the desktop?

just install "gnome-tweak-tool" and turn it on. You have to enable "Have file manager handle the desktop".

It's easier to set the appropriate gconf key with the following command:

gsettings set org.gnome.desktop.background show-desktop-icons true

Update Jan 2019

GNOME 3.28 has removed the ability to place files on the desktop (rationale, annoucement).

Install the "Desktop icons" GNOME shell extension (GNOME extensions website, git).