Ask HN: How to automatically mirror your own sites?

As my business grows, I want to rely less on one hosting service. Ideally I want to set up a failover system for my VPS so that if one host goes down, the other seamlessly gets traffic redirected to it.

I'm not sure this is actually possible--even if I get servers to stay roughly in sync, what happens when the primary server goes down but the DNS servers pointing at it are fine?

The first problem is actually mirroring everything automatically. How can I keep copies of the files and database in sync across disparate hosting services?

The second problem is how I set up the DNS to fail over to the mirror site.

Is this feasible?