Our server has been able to handle tons of hits (like 6 requests per second at peak) but the DNS acts flimsy under pressure. We just have the server handling it at the moment.
If you have multiple web servers servers in different locations, you might be thinking of "Geo-DNS" -- this actually directs the end user to the nearest web server. There are pros and cons to this approach, namely that the end user may be using an intermediary DNS server that's not actually very close to the user. For example, you might end up sending all Comcast users to your east coast USA server, no matter where in the USA they actually are. I'm not familiar with providers who offer this service, but here's a Server Fault thread on the matter: http://serverfault.com/questions/30567/geo-dns-providers