Bowing -- The main form of greeting in Japan is the bow rather than the handshake. Although at first glance it may seem simple enough, the bow -- together with its implications -- is actually quite complicated. The depth of the bow and the number of seconds devoted to performing it, as well as the total number of bows, depend on who you are and to whom you are bowing. In addition to bowing in greeting, the Japanese also bow upon departing and to express gratitude. The proper form for a bow is to bend from the waist with a straight back and to keep your arms at your sides, but as a foreigner you'll probably feel foolish and look pretty stupid if you try to imitate what the Japanese have spent years learning. A simple bob of the head is enough. Knowing that foreigners shake hands, a Japanese person may extend a hand but probably won't be able to stop from giving a little bow as well. I've even seen Japanese bow when speaking to an invisible someone on the telephone.
http://travel.nytimes.com/frommers/travel/guides/asia/japan/tokyo/frm_tokyo_0085022417.html
I have YET to see a picture of a head of state or foreign royalty visit the Emperor in Japan and submit to this ignorant if not outrageous national humiliation of their own country they go abroad to represent. Obama just did.