While you wouldn't usually want non-privileged user to reload a Cisco IOS-based router, you might also not appreciate the need to give the network operator level-15 access (which includes configuration privileges) just to reload the box. The solution is the privilege configuration command. To lower the privilege level of the reload command, configure privilege exec level desired-level reload. For example, after configuring ...

privilege exec level 4 reload
enable secret level 4 mypassword

... an operator can reload the box with the following commands:

Rtr>enable 4
Password:
Rtr#reload
System configuration has been modified. Save? [yes/no]: n
Proceed with reload? [confirm]y
14:11:13: %SYS-5-RELOAD: Reload requested by console.

Note: this article is part of You've asked for it series.