I also have this problem, particularly with HTTPS. The DNS address of the destination is an akamai cache and not the true destination, and the cache is serving no data. That's what I am finding anyway.
Affected for me are:
santander.co.uk
community.bt.com (ironic!)
twitpic
Today is day two of infinity, not going well so far!
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Hardware:
P4 2.83gz Quad core. 8GB DDR/1066mhz Ram.
3.7tb Raid 0+1 HD Storage