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Not sure what types of volume you are talking about but traditional hosting companies like hostgator, rackspace and others typically want to charge you extra for anything outside the box (ie load balancing, database support, etc.) We have had most of our luck using companies that specialize in moving video content, because they are already set up to handle huge workloads and traffic. Company we use is advection.net. Very affordable and most importantly reliable...
Mark
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This looks like an older thread.... but for what it's worth we've driven 100K clicks a day through LiquidWeb. Their support is the best in the business from what I've experienced. We have a dedicated on their Storm On Demand system which allows you to scale up infrastructure within minutes. They're awesome.
I've also heard Beyond Hosting has very fast redirects and capacity as well.