As U.S. oil fell to a six-year low below $41 a barrel on Wednesday, an increasing number of analysts and traders are saying crude could drop into the $30s—and soon.

The move to a price last seen at the height of the financial crisis, in February 2009, could come amid a seasonal falloff in demand, coupled with concerns about the Chinese economy and the continuing global glut of crude. Cheaper oil would bring further joy to consumers and businesses around the globe, but more pain for everyone from Russian budget officials to...