How to shutdown and reboot without sudo password

First of all you need sudo package.

apt-get install sudo

Modify /etc/sudoers with visudo.

# Cmnd alias specification
Cmnd_Alias SHUTDOWN_CMDS = /sbin/shutdown, /sbin/reboot

# User privilege specification
user1  ALL= NOPASSWD: SHUTDOWN_CMDS

Now user1 is able to restart:

user1@deby:~$ sudo /sbin/reboot

Broadcast message from root@deby (pts/0) (Sat Apr 24 00:06:53 2010):

The system is going down for reboot NOW!

or shutdown the system without sudo password:

user1@deby:~$ sudo /sbin/shutdown -h now