Common as well in first-millenium middle-east, as in Petra[0] or Mada'in Saleh[1], and there were quite a few cliff-dwelling people in precolumbian north-america, the most well known probably being the Anasazi which had well-known under-outcropping dwellings (e.g. Cliff Palace) but also actual cave dwellings like Tsankwawi[2] or very-close-to-cave dwellings like the House of Many Windows[3].

[0] http://en.wikipedia.org/wiki/Petra

[1] http://en.wikipedia.org/wiki/Mada%27in_Saleh

[2] http://en.wikipedia.org/wiki/Tsankawi

[3] http://en.wikipedia.org/wiki/File:House_of_Many_Windows.JPG