It may be necessary to monitor SSH login attempts or especially successful logins for specific users (e.g. root). To that end, it is possible to be notified by email for each successful login. Follow the SSH article to achieve that. To monitor the online status of the SSH server, you may use a service like the Uptime Robot.
It is especially useful to monitor whether the web server is still online or not. To that end, one may use services like Uptime Robot.
The Uptime Robot can monitor whether the mail server is still up and running or not, too.
The Uptime Robot can monitor whether the database server is still up and running or not, too.