The latest update from the Netflix Community Blog notes that they've started shipping DVDs again from some locations:
By late this afternoon, we’d made enough progress on our system issues to begin shipping again from some of our distribution centers. We hope to bring the rest of our facilities back online overnight and be shipping from all of our distribution centers on Friday. But the issues we’ve faced over the last several days have been significant and there’s no guarantee at this point that our shipping operations will be fully restored by tomorrow. We’ll again be working throughout the night and will update you in the morning. Thanks for now and continued apologies.
Netflix is lucky that this happened during the Olympics -- I'm wondering how many customers noticed that there was a problem.