Frightened ostriches do not bury their heads in the sand. They run from danger. But the myth may have started because of the way the birds try to protect their nests from predators. Both males and females lie flat on the ground, necks outstretched, to avoid detection. Pliny the Elder wrote about ostriches in 100 AD, but he claimed they hid their heads in bushes. Sometime in the 1400s, 'bushes' was changed to 'sand.'
Sources: World Wildlife Fund Web site; Encyclopedia Britannica; 'The Ostrich Factor,' by Garrett Hardin; the Canadian Museum of Nature online.