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Significant, but limited in duration to a month or two according to much of what I have read. Efforts to restore production are already taking place, to the point that a few days ago divers were sent underwater into the production facilities to retrieve vital production equipment, which is pretty surreal if you think about it. Part of the problem is the Western Digital manufactures about half of the world's disks, and their Thai facility accounts for about half of Western Digital's production, and they apparently located the Thai facility on a flood plain. Oops. There goes about a quarter of earth's disk supply for a couple months. I'm not sure how much other manufactures can scale up production, but I bet it won't cover the shortfall.
There are other problems associated with the flooding beyond disk manufacturers - component manufactures located in the same area. The manufacturer of most of the spindle motors is also in the flood area. So there is another monkey wrench in the supply chain.
In the short term, the best answer for someone needing a drive may be SSDs. But that is a compromise of less storage and more performance, so it will work for some applications and not for others. In the current economy, I'm a little concerned about the effect on retail sales right at the the holiday season, which is so critical for most retail companies.