Shutdown the computer as an unprivileged user from X

Jessie

Use systemctl to power off, reboot, suspend, or hibernate the system:

$ systemctl poweroff
$ systemctl reboot
$ systemctl suspend
$ systemctl hibernate

Note: This method works only for locally loged-in users.

Prerequisites

systemd must be installed and used as a system and service manager (default in jessie)
policykit-1 must be installed (automatically installed with any (?) desktop environment)

References

Archwiki

Wheezy and Earlier

Shutting down as a user doesn't work out of the box if you are not using one of the big desktop environments. To enable shutdown as user you mus make sure that

dbus is running
consolekit is used.

If you are not using gdm or kdm but xdm or startx, in ~/.xinitrc prepend the line starting your window manager with ck-launch-session , e. g.

exec ck-launch-session icewm-session

Then you can use following commands:

shutdown

dbus-send --system --print-reply --dest="org.freedesktop.ConsoleKit" /org/freedesktop/ConsoleKit/Manager org.freedesktop.ConsoleKit.Manager.Stop

reboot

dbus-send --system --print-reply --dest="org.freedesktop.ConsoleKit" /org/freedesktop/ConsoleKit/Manager org.freedesktop.ConsoleKit.Manager.Restart

suspend

dbus-send --system --print-reply --dest="org.freedesktop.UPower" /org/freedesktop/UPower org.freedesktop.UPower.Suspend

consolekit > 0.4.1

If you use consolekit > 0.4.1 (wheezy and newer) this doesn't work any more out of the box. To get it working again add

session optional        pam_loginuid.so