Although I sometimes get downvoted for this, I'll say it again: You can't outsource your liability. If your product is a webapp, then the underlying messy bits of backups, hardware, availability and redundancy also require some amount of conscious thought on your part. Not every site/app needs it's own mini-datacenter, and you might not even need your own dedicated server (though you probably do when you reach a cert…
You can't outsource your liability. Of course you can. That is the entire reason the insurance industry exists. More practically for the instant case, I use a provider who has a turnkey backup option, rather than one which would force me to spend expensive engineer time rolling my own only to discover that I really suck at thinking through all of the design challenges of backup solutions. (Something which always seem…
The Internet is filled with news about hosting provider provided backups being unusable for a number of reasons at inopportune times.
You should have a backup copy of your code/databases in your control, on a machine that is completely independent from whatever you are doing your production hosting on. You should have done a "warm metal" install and test of that code another server to be sure that you can recover operations in a reasonable amount of time (whatever is appropriate for your case).
For your scale (based on your posts here, my assumption: Single developer, or developer with a couple of contractors; production site; 1-5K visits per month; non time-sensitive/mission-critical service.) you probably don't need high-availability auto-failover. But, you SHOULD have your DNS hosted separate from your hosting provider, you SHOULD have low TTL's, you SHOULD have a backup server in a warm state at some other provider, and you SHOULD know how to at least do a basic DNS update to redirect traffic over to a backup site that either runs the service or puts up a basic, friendly "OOPS, BRB" page.
I've often thought of a startup that would basically human-automate these things for guys like you. You still wouldn't be 100% self-sufficient, but you would be able to outsource SOME of your entire reliance on 1 provider. You'd then have to have 2 tiers of total failure (your provider, and this service) to encounter complete down time.