How can I use Adwaita Dark for all applications in Gnome 3?

Replacing the main theme with the dark one in /usr/share/themes is not an ideal solution as each time gnome-themes is updated your theme will revert to default. It's preferable to properly configure your user account to use the dark theme, that way your settings will be preserved between updates. You can do that:

• Manually: create (open if already present) the following file:

  ~/.config/gtk-3.0/settings.ini

  edit like this:

  [Settings]
gtk-application-prefer-dark-theme=1

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• Via gnome-tweak-tool (which essentially does the same thing as above, writing the same file):

  

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GTK2 Problem

This answer is indeed the ideal and "safe" (i.e no need to replace/mod any system files) method. However, currently neither this method nor Jeff's answer works for all apps. Coz only GNOME3/GTK3 has support for the dark theme mode. As of now, there are still many apps (for example those written in GNOME2/GTK2, Qt, wxWidgets, Java, etc) which don't use GTK3 and remain on the old GTK2 theming. To make those apps dark, replacing/modding the GTK2 part($ACTIVE_THEME/gtk-2.0/gtkrc) of the currently active theme works. To know more, see the answer to "Firefox not affected by gtk theme".

As GTK2 is deprecated and superseded by GTK3, all actively developed GTK2 apps are getting ported to or replaced by GTK3. Sooner or later, other toolkits like Qt, wxWidgets, etc may also implement support for GTK3. By that time, this method may become valid for all(maybe almost all) apps.

Simply replace the main theme with the dark one (in a special copy of Adwaita in your home dir):

mkdir -p ~/.themes
cp -r /usr/share/themes/Adwaita ~/.themes/Darkwaita
cd ~/.themes/Darkwaita/gtk-3.0
cp gtk-dark.css gtk.css

Then use a tool like gnome-tweak-tool to set Darkwaita as your gtk theme, and the changes should take effect immediately.