This nice little video, dredged up by Kottke.org, threw me for a loop when I first saw it. It took me back to 1988, when I was in Japan and saw Japanese students, workers, and housewives doing multiplication like this so swiftly and confidently it blew my mind. To see it again, and explicated slowly and clearly, settled some neurotransmitter flotsam into place, at long last. A fascinating alternative to stacked numbers.
Now, try 458 x 16 using this technique, just for the fun of it.