Sensor size. Depth of field is based on (1) sensor size (you want big), (2) aperture (you want a low number, i.e. big opening), (3) focus distance to nearest subject, and (4) focal length (I think...).
So on a full frame sensor camera, shooting someone's portrait with an 80mm will give you very shallow DoF, on a sensor the size of an iPhone, it's probably close to infinite.
Edit: I don't think the above is technically exactly correct...Here's a good explanation: http://www.cambridgeincolour.com/tutorials/depth-of-field.ht...