While this is possible, it requires shared storage, which is a single point of failure, and can be quite expensive. None of the VPS providers I know of support live migration. I know I don't.
Also, live migration doesn't help you of the hardware dies. (I mean, if the host is using shared storage, it is easy to bring you up on a new host, but you still crashed. you can run a dedicated off shared storage, if that is all you want.) You can only 'live migrate' off a 'live' host. Now, if you wanna get really expensive, vmware (and xen, if you want to do some patching) has the capability to essentially 'live migrate every Xms' - the idea being that they never bring up the second host unless the primary host fails; but it's ready, and only Xms behind. (they do some things I don't understand to insure that I/O to the shared block device is in sync) This is very expensive, though, because not only do you need to pay for 2x the hardware, you need a vmware license. (or to run a non-standard xen)
A dedicated server with mirrored drives and ecc ram is likely going to be more reliable than a VPS.