updated 08:13 pm EDT, Wed March 12, 2014
Fault is likely due to hacker attack rather than Apple-originated issue
[Update: attack over] Users around the world -- particularly those who rely on Google DNS or Speakeasy to provide their DNS connections -- were seeing some (but not all) of Apple's websites blocked. In particular, the attack seems focused on Apple.com and iTunes, with other services such as iMessage and Game Center seemingly unaffected. The attack is now over, but it remains unclear if Google DNS was the source of the issue or just the first to propagate the bad DNS entries.
In the US, issues were being seen with Google, Mindspring, Sprint, Verizon, and Speakeasy, though the list of affected providers changed constantly. The problems apparently began around 6:36PM Eastern, but Apple's system status page shows all services operating normally, indicating that the issue is only coming from bad DNS entries rather than any problems on Apple's end.
The connecting issues were described as "intermittent" by users taking to Twitter and other outlets to report outages, and DNS reports show shifting issues with ISPs around the globe as the bad DNS entries propagate. The event was over by 10PM EST, with no clear reason for the poisoned DNS.