There are a lot of reasons why you should monitor your Drupal sites.
"Know where the fire is"
When a Drupal site is down, you should immediately receive an alert (sms, email, tweet) so you can react and fix the problem. Especially when you run a lot of Drupal sites, it's hard to manually test the sites. Using a monitoring tool helps you to see if all your sites are "OK" or not, just from one dashboard. Without monitoring, your Drupal portfolio is just a big black hole.
Todays websites are complex. The are not just a bunch of HTML sites, they are rich applications with lots of functionality. A lot of security issues can come up if your Drupal modules and the underline webstack is not updated. It's important to know wheater your Drupal core or Drupal modules are up to date and need security patches. Without monitoring, you never know if one of your site got hacked soon.
This might not be an issue for very small sites, but for bigger sites, capacity planning is crutial. There are several metrics which are interesting to look at like disk usage, cpu load, number of queries per second, number of page requests, php max memory usage, number of enabled modules, etc. This data let's you plan if the current server system has enough power to server future traffic or more storage on the webserver. Without monitoring, you never know when you need more disk space, a more powerful machine, a fater internet connection.
Your site can be done as shiny as possible, if it does not load fast, you loose traffic. Performance is crutial and you should monitor your page load times, enable and check cache settings, sloq queries etc. over time.
Websites can be hacked and missused. This can harm your brand and customer loyality. You better know right away, if somebody unwanted changed contents, replace the frontpage with bad content or the like.
Bonus: I only use my website for private use, so I don't care...
Ok - there is no international rule for website monitoring. But bear in mind, your website can be abused as spam zombie, link farm or malware distribution warehouse.