This is probably a case of "if I new what it was called, I could google it in 5 minutes" - but I don't know what it's called.
It's probably best to explain the requirement using an example. We have a number of services (vpn, owa, etc) which we host from one of our datacenters. We have a number of datacenters, and we technically have the infrastructure already in place to support these services at a number of our datacenters. To provide access to these "services", I would create an external DNS entry (ex. VPN.MyCompany.com > Gateway IP for one of my DCs), and clients will connect to it via the DNS entry. Since I have multiple datacenters that can support this service, I could theoretically offer a "highly available, geographically dispersed" solution if I could point this DNS entry to some sort of third party who offers highly available "redirection" services. If my primary site goes down, I could just make a change via some management console and configure the redirector to point to a different DC. Of course, it would be fairly straightforward to set this sort of thing up on one of our servers, but that would kinda defeat the purpose of a highly available third party.
Is anyone familiar with a service like this? I'm thinking something like DynDNS, but with Enterprise availability guarantees.
Don't know the services off hand, but I think you may want to learn a little bit how multi-site redundancy can be done. The two big methods I have read about are:
The DNS solutions are probably going to be a lot cheaper, if you can even purchase BGP options? Here is a post about the DNS Trickery method.
TZO.com is another provider you can have a look at. This is probably their offering that you'll want to look at http://www.autofailover.com/
You want enterprise, look at our (Dyn Inc.'s) Dynect Platform. It's the premium anycast version of DynDNS with advanced features like failover and GSLB. http://dyn.com/dynect
You can google for GSLB aka Global Server Loadbalancing which is the DNS 'Trickery' Option and also what akamai and wikipedia use.
Look at http://wiki.powerdns.com/trac/browser/trunk/pdns/modules/geobackend/README for a short technical introduction to the topic.
BGP Failover might be suited for your, that is announcing one prefix with a lower metric than the other which in turn will get all the traffic unless that site is offline and hence the lower metric BGP announcements are missing from the global routing table. BGP Anycasting i.e. announcing one prefix at several sites with the same metric/localpref in general is not suitable for anything other DNS actually as you can not control who gets it over which line.