If you're just looking to have it on "stand-by" I suppose you can accomplish this well enough (depending on what your uptime requirements are) using DNS. Simply point the domain to a new IP when the change is required. But I know this is manual.
Barring that, enterprise level load balancers exist that can do the same, I've seen some in a few client environments, but never for failover, mostly it's geographical or performance-based decisions per user on which datacenter will service said user. That said, I know you can configure load balancing per host to work in many different ways on most devices, including active/passive (failover) so I'm sure the same can be done but in terms of what site instead of what host. I'm purposely avoiding recommending any one/some brands due to potential perception of conflict of interest at work.
An alternative would be to use a CDN, if the budget exists for it. I can't speak for others, but I've worked with Akamai for joint clients and they have a site failover service which you may find useful. Check out http://www.akamai.com/html/technology/products/site_failover.html for an example