It depends a lot upon your time frame and your definition of 'thrived,' but generally cheap vices and those companies which supported cheap vices continued to be profitable during the Great Depression. By 'cheap vices' I mean things like tobacco and sweets.

Companies which produced sugar, fats and oils, as well as tobacco, handled the downturn much better than typical cyclical companies. The forestry firms Diamond Match and Mengel Company supported these industries. Diamond made matches for smokers and Mengel made packing materials for things like soap and tobacco. They both did quite well 1930-1932.

The idea is that in times of severe economic downturns people still like to have cheap luxuries, like a smoke or a piece of candy now and then. They might not be able to afford a new car, but they could afford a cigar or two.

Source: Jason Zweig, Center for Research in Security Prices at the University of Chicago's Booth School of Business and the Wall Street Journal