[Animats]

I usually use "http://www.downforeveryoneorjustme.com/".

If your site's back end is down, the site itself should be saying something intelligent. ("Ngnix timeout", or Cloudflare's error message blaming the site server, is kind of lame, but it's something.)

[jacques_chester]

Cloudflare will serve any page you like during an outage.

If you pay them.

[gkoberger]

Sites aren't all or nothing. It's possible something like just image uploads might be broken, or maybe you want to keep people updated as the issues progress.