For clients it's really important to report to them monthly on their stats so they know how many visitors, how often the site went down etc. So I may credit them for future services if need be.
But for my own sites I'm not too worried. I've got Cloudflare installed server wide so if it goes down at least they get a message.
I do because in summer/fall 2014 my previous host was getting hit with DDoS attacks which meant we were going down with no idea why or for how long. (June 2014 we had 24 hours of downtime...) So I started using Pingdom to at least check to see how long the outages were.
Pingdom used to offer the option to sign up for a free service. However I don't know if they still do anymore or not. I can't seem to find the spot to sign up for a free account. (It just says start off for a 14 day free trial. I presume after that 14 day trial ends you're dropped to a free account... but I have no idea. I'd be careful just to ensure I wasn't getting billed though.)
Another option I've heard good things about is statuscake.com.
They still have a free option for existing free customers but it has less features due to a recent change. I am not sure if you can get a free account as a new user though.