How do I shutdown, restart, or log off Windows via a bat file?

Question

The most common ways to use the shutdown command are:

shutdown -s — Shuts down.
shutdown -r — Restarts.
shutdown -l — Logs off.
shutdown -h — Hibernates.

Note: There is a common pitfall wherein users think -h means “help” (which it does for every other command-line program… except shutdown.exe, where it means “hibernate”). They then run shutdown -h and accidentally turn off their computers. Watch out for that.
shutdown -i — “Interactive mode”. Instead of performing an action, it displays a GUI dialog.
shutdown -a — Aborts a previous shutdown command.

The commands above can be combined with these additional options:

-f — Forces programs to exit. Prevents the shutdown process from getting stuck.
-t <seconds> — Sets the time until shutdown. Use -t 0 to shutdown immediately.
-c <message> — Adds a shutdown message. The message will end up in the Event Log.
-y — Forces a “yes” answer to all shutdown queries.

Note: This option is not documented in any official documentation. It was discovered by these StackOverflow users.

I want to make sure some other really good answers are also mentioned along with this one. Here they are in no particular order.