Run / Execute Command Using SSH

How do I run a command using ssh under UNIX, OS X, and Linux operating systems?

The SSH client program can be used for logging into a remote machine or server and for executing commands on a remote machine. The syntax is as follows for executing commands:
ssh user1@server1 command1
ssh user1@server1 'command2'
ssh user1@server1 'command1 | command2'
The ssh client will login to a server called server1, using user name called user1 and run a command call command1.

Examples

Get remote server date and time:

ssh user1@server1 date

Find out remote server disk space usage:

ssh user1@server1 'df -H'

Run a script called /scripts/backup.sh:

ssh operator@oracle1  '/scripts/backup.sh'