Perhaps I should clarify a little bit further.
Been running a hosting company for 16 years, all on dedicated equipment. Never ran the host on a VPS or reseller account, or anything silly like that. In those 16 years, I have never had a server fail. Nope, not one. Sure, hard drives go bad. That's what RAID10 arrays are for. I've had memory sticks crap out. You replace them. Even had power supplies blow up (one, I was told by the datacenter folk, looked like a lightning storm inside the rack), but that's what redundant supplies are for. All the datacenters I deal with have around a 15 minute SLA on hardware replacement.
If a server was to completely blow up, I'd slap the drives in a brand new server, and off we go. Good as new. You're talking 15-30 minutes max. Then of course, you get into cloud hosting, where it doesn't matter in the slightest if a single server goes down. Doesn't affect the clients at all.
Secondly, how often do entire datacenters go offline? No doubt it happens in cheap datacenters, but when you use quality datacenters, it should never happen. Most have at least a half dozen different network/bandwidth providers, so if one of them (or even 5 of them) should go out, it doesn't matter. All have multiple forms of redundant power, etc. The only time you're going to get a datacenter outage is when something really, really bad happens, like a natural disaster. If an entire datacenter was to just fall off into the ocean, we could have our clients up and running on new servers in an alternate datacenter in a very short time.
That was actually a concern for us prior to Hurricane Irene last year, since we use Equinix New York for a handful of servers. We have a couple servers in the Softlayer DC center now as well, so that location is obviously a concern too. In our testing, we were able to restore user accounts, from our backups (which we take every hour) to new servers in other locations in just a matter of minutes.
Failover DNS is great for companies with absolutely no contingency plan for disaster recovery. In reality, there should never be a time where a server is inaccessible for more than 15-30 minutes, and the proverbial you know what should have to hit the fan to get to that point.